Simple Acceleration Problem throwing me off - Physics Stack Exchange most recent 30 from physics.stackexchange.com 2019-08-17T13:12:08Z https://physics.stackexchange.com/feeds/question/77582 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://physics.stackexchange.com/q/77582 0 Simple Acceleration Problem throwing me off fnsjdnfksjdb https://physics.stackexchange.com/users/29738 2013-09-17T00:40:01Z 2013-09-18T04:46:41Z <p>I am having trouble with this problem from my homework. I have gone over it many times, and I must have some concept wrong. </p> <p>A rocket is launched from the ground with constant acceleration. After 4 seconds, a bolt falls off and hits the ground 6 seconds later. Gravity is -9.8m/s^2. What was the rocket's acceleration?</p> <p>So here's my thoughts. </p> <h2>First, let's get the height of the rocket when the bolt falls.</h2> <p>Fell at 9.8m/s^2 for 6s, so the final velocity was 58.8m/s</p> <p>Average velocity was half of that, because of the constant acceleration, so 29.4m/s</p> <p>Total distance is that average, times 6 seconds, 176.4m.</p> <p>Good so far?</p> <h2>Next, the rocket's acceleration</h2> <p>We know it was 176.4m in the air after 4 seconds.</p> <p>So the average velocity 44.1 m/s, final velocity is 88.2 m/s</p> <p>It got to that in 4 seconds, so the acceleration must be 22.05 m/s^2</p> <p>But it's not. The correct answer is 5.5 m/s^2, a quarter of what I got.</p> <h2>So what went wrong?</h2> <p>I've tried looking through all the steps a bunch of times, and I can only think of one step that doesn't seem quite right. The bolt falling off the rocket makes it sound like it just drops, but maybe it starts that drop with an upwards velocity?</p> <p>But I can't see any way of getting to that velocity. Without knowing how high the rocket is, we can't know how fast it's going, so we can't know how fast the bolt was moving upwards. And then we have two variables in the equation, and an infinite number of correct pairs.</p> <p>I must be missing some concept, some formula must be missing. Can you find it?</p> https://physics.stackexchange.com/questions/77582/-/77589#77589 1 Answer by Alfred Centauri for Simple Acceleration Problem throwing me off Alfred Centauri https://physics.stackexchange.com/users/9887 2013-09-17T02:16:40Z 2013-09-17T02:16:40Z <p>Since the initial speed an position are zero, the position and upward velocity after 4 seconds are:</p> <p>$z(4) = \dfrac{a_1 (4s)^2}{2}$</p> <p>$v(4) = a_1 (4s)$</p> <p>When the bolt falls off, the acceleration changes from $a_1$ to $-9.8\dfrac{m}{s^2}$ and the bolt impacts the ground 6 seconds later. So...</p> <p>$z(10) = 0 = z(4) + v(4)\cdot 6s - 9.8\dfrac{(6s)^2}{2} = \dfrac{a_1 (4s)^2}{2} + a_1 (4s)\cdot6s - 9.8\dfrac{(6s)^2}{2}$</p> <p>Solve for $a_1$.</p>