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Cleaned up tex a bit
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Brandon Enright
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If you are limiting the takeoff speed to prevent it bottoming out, then I suggest you lower the ramp. 45 degrees$45^\circ$ gives optimal range for a given takeoff speed (ignoring friction), but only if you don't care what the vertical component of the velocity is on landing.

At 30 mph$30\: \mathrm{mph}$, with a 45 degree$45^\circ$ jump, you say it doesn't bottom out. The vertical component of the velocity on landing has approximately the same magnitude as on take off (air resistance losses), which would be $30 \; cos(45)$$30 \; \cos(45^\circ)$ = about 26 mph$26\: \mathrm{mph}$.

To maximise the range, then, we need to keep this vertical component ($v_y = 26 \mathrm{mph}$$v_y = 26\: \mathrm{mph}$), whilst letting the overall speed ($v$) increase to 45 mph$45\: \mathrm{mph}$.

$v^2 = v_x^2 + v_y^2$

$v_x^2 = v^2 - v_y^2 = 45^2 - 26^2 = 1349$

$v_x = \sqrt{1349} = 36.7 \mathrm{mph} $

So we can calculate the angle from the $x$ and $y$ components of the velocity:

$\tan(\theta) = v_y / v_x = 26 / 36.7 = 0.71$

$\theta = \arctan(\theta) = \arctan(0.71) = 35^{\circ}$

So based on that information, try 35 degrees$35^\circ$, with a speed at the ramp of 45 mph$45\: \mathrm{mph}$.

If you are limiting the takeoff speed to prevent it bottoming out, then I suggest you lower the ramp. 45 degrees gives optimal range for a given takeoff speed (ignoring friction), but only if you don't care what the vertical component of the velocity is on landing.

At 30 mph, with a 45 degree jump, you say it doesn't bottom out. The vertical component of the velocity on landing has approximately the same magnitude as on take off (air resistance losses), which would be $30 \; cos(45)$ = about 26 mph.

To maximise the range, then, we need to keep this vertical component ($v_y = 26 \mathrm{mph}$), whilst letting the overall speed ($v$) increase to 45 mph.

$v^2 = v_x^2 + v_y^2$

$v_x^2 = v^2 - v_y^2 = 45^2 - 26^2 = 1349$

$v_x = \sqrt{1349} = 36.7 \mathrm{mph} $

So we can calculate the angle from the $x$ and $y$ components of the velocity:

$\tan(\theta) = v_y / v_x = 26 / 36.7 = 0.71$

$\theta = \arctan(\theta) = \arctan(0.71) = 35^{\circ}$

So based on that information, try 35 degrees, with a speed at the ramp of 45 mph.

If you are limiting the takeoff speed to prevent it bottoming out, then I suggest you lower the ramp. $45^\circ$ gives optimal range for a given takeoff speed (ignoring friction), but only if you don't care what the vertical component of the velocity is on landing.

At $30\: \mathrm{mph}$, with a $45^\circ$ jump, you say it doesn't bottom out. The vertical component of the velocity on landing has approximately the same magnitude as on take off (air resistance losses), which would be $30 \; \cos(45^\circ)$ = about $26\: \mathrm{mph}$.

To maximise the range, then, we need to keep this vertical component ($v_y = 26\: \mathrm{mph}$), whilst letting the overall speed ($v$) increase to $45\: \mathrm{mph}$.

$v^2 = v_x^2 + v_y^2$

$v_x^2 = v^2 - v_y^2 = 45^2 - 26^2 = 1349$

$v_x = \sqrt{1349} = 36.7 \mathrm{mph} $

So we can calculate the angle from the $x$ and $y$ components of the velocity:

$\tan(\theta) = v_y / v_x = 26 / 36.7 = 0.71$

$\theta = \arctan(\theta) = \arctan(0.71) = 35^{\circ}$

So based on that information, try $35^\circ$, with a speed at the ramp of $45\: \mathrm{mph}$.

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Phil H
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If you are limiting the takeoff speed to prevent it bottoming out, then I suggest you lower the ramp. 45 degrees gives optimal range for a given takeoff speed (ignoring friction), but only if you don't care what the vertical component of the velocity is on landing.

At 30 mph, with a 45 degree jump, you say it doesn't bottom out. The vertical component of the velocity on landing has approximately the same magnitude as on take off (air resistance losses), which would be $30 \; cos(45)$ = about 26 mph.

To maximise the range, then, we need to keep this vertical component ($v_y = 26 \mathrm{mph}$), whilst letting the overall speed ($v$) increase to 45 mph.

$v^2 = v_x^2 + v_y^2$

$v_x^2 = v^2 - v_y^2 = 45^2 - 26^2 = 1349$

$v_x = \sqrt{1349} = 36.7 \mathrm{mph} $

So we can calculate the angle from the $x$ and $y$ components of the velocity:

$\tan(\theta) = v_y / v_x = 26 / 36.7 = 0.71$

$\theta = \arctan(\theta) = \arctan(0.5) = 35^{\circ}$$\theta = \arctan(\theta) = \arctan(0.71) = 35^{\circ}$

So based on that information, try 35 degrees, with a speed at the ramp of 45 mph.

If you are limiting the takeoff speed to prevent it bottoming out, then I suggest you lower the ramp. 45 degrees gives optimal range for a given takeoff speed (ignoring friction), but only if you don't care what the vertical component of the velocity is on landing.

At 30 mph, with a 45 degree jump, you say it doesn't bottom out. The vertical component of the velocity on landing has approximately the same magnitude as on take off (air resistance losses), which would be $30 \; cos(45)$ = about 26 mph.

To maximise the range, then, we need to keep this vertical component ($v_y = 26 \mathrm{mph}$), whilst letting the overall speed ($v$) increase to 45 mph.

$v^2 = v_x^2 + v_y^2$

$v_x^2 = v^2 - v_y^2 = 45^2 - 26^2 = 1349$

$v_x = \sqrt{1349} = 36.7 \mathrm{mph} $

So we can calculate the angle from the $x$ and $y$ components of the velocity:

$\tan(\theta) = v_y / v_x = 26 / 36.7 = 0.71$

$\theta = \arctan(\theta) = \arctan(0.5) = 35^{\circ}$

So based on that information, try 35 degrees, with a speed at the ramp of 45 mph.

If you are limiting the takeoff speed to prevent it bottoming out, then I suggest you lower the ramp. 45 degrees gives optimal range for a given takeoff speed (ignoring friction), but only if you don't care what the vertical component of the velocity is on landing.

At 30 mph, with a 45 degree jump, you say it doesn't bottom out. The vertical component of the velocity on landing has approximately the same magnitude as on take off (air resistance losses), which would be $30 \; cos(45)$ = about 26 mph.

To maximise the range, then, we need to keep this vertical component ($v_y = 26 \mathrm{mph}$), whilst letting the overall speed ($v$) increase to 45 mph.

$v^2 = v_x^2 + v_y^2$

$v_x^2 = v^2 - v_y^2 = 45^2 - 26^2 = 1349$

$v_x = \sqrt{1349} = 36.7 \mathrm{mph} $

So we can calculate the angle from the $x$ and $y$ components of the velocity:

$\tan(\theta) = v_y / v_x = 26 / 36.7 = 0.71$

$\theta = \arctan(\theta) = \arctan(0.71) = 35^{\circ}$

So based on that information, try 35 degrees, with a speed at the ramp of 45 mph.

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Phil H
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If you are limiting the takeoff speed to prevent it bottoming out, then I suggest you lower the ramp. 45 degrees gives optimal range for a given takeoff speed (ignoring friction), but only if you don't care what the vertical component of the velocity is on landing.

At 30 mph, with a 45 degree jump, you say it doesn't bottom out. The vertical component of the velocity on landing has approximately the same magnitude as on take off (air resistance losses), which would be $30 \; cos(45)$ = about 26 mph.

To maximise the range, then, we need to keep this vertical component ($v_y = 26 \mathrm{mph}$), whilst letting the overall speed ($v$) increase to 45 mph.

$v^2 = v_x^2 + v_y^2$

$v_x^2 = v^2 - v_y^2 = 45^2 - 26^2 = 1349$

$v_x = \sqrt{1349} = 36.7 \mathrm{mph} $

So we can calculate the angle from the $x$ and $y$ components of the velocity:

$\tan(\theta) = v_y / v_x = 26 / 36.7 = 0.71$

$\theta = \arctan(\theta) = \arctan(0.5) = 35^{\circ}$

So based on that information, try 35 degrees, with a speed at the ramp of 45 mph.