# Question based on relative motion in two dimension

I came across this problem in my work book.

A hunter is riding on an elephant of height $4$ $m$ moving in straight line with uniform speed of $2$ $m/s$. A deer running with a speed $V$ at a distance of $(4$ $\sqrt{5}$ $) m$ moving perpendicular to direction of motion of the elephant. If hunter can throw his spear with a speed $10$ $m/s$ relative to elephant, then at what angle to its direction of motion must he thrown w.r.t elephant his spear horizontally for a successful hit. Find also the speed $V$ of deer.

I tried drawing the diagram as shown below : $v_e$ is the velocity of the elephant, $v_s$ is the absolute velocity of the spear and $v_{se}$ is the relative velocity of the spear with respect to the elephant.

Since the deer is moving perpendicular to the elephant, if the elephant is moving in the $Y$ axis, the deer must have been standing on the $Y$ axis at $(4$ $\sqrt{5}$ $) m$ and running parallel to the $X$ axis. The spear must be thrown at an angle to hit the deer.

As the spear and the deer will clearly meet after $t$ seconds, by Pythagoras' theorem

$(v_s . t)^2$ - $(V.t)^2$ = 80

$\lvert v_s \rvert$ = $\sqrt{100+4+40 cos \theta}$

From here, I am unable to proceed. I feel there are too many variables to solve. Could anyone help ?

• "...hunter can throw his spear with a speed $10 m/s$..." – Yuzuriha Inori Apr 11 '18 at 5:25
• @YuzurihaInori Sorry, I did not understand. $10$ $m/s$ is said to be the relative speed and not the absolute speed – Fasal123 Apr 11 '18 at 5:31
• There are too many unknowns. However, you might consider using the extra information of elephant height. The spear is said to be thrown horizontally. The hunter would know what should be the spear's height at impact. Say $1m$. From this, you can gather the time of flight $t$. A bit far fetched solution for a physics problem. – npojo Apr 11 '18 at 12:45