First slide

Projectile motion

Question

A ball is projected horizontally from an incline so as to strike a cart sliding on the incline. Neglect height of cart and point of projection of ball above incline. At the instance the ball is thrown, the speed of cart is v (in m/s). Find v so that the ball strikes the cart.

Difficult

A

4
B

6
C

2
D

8

Solution

Time of flight:
$\begin{array}{l} T = \frac{2 v_{0} \sin 37^{\circ}}{g \cos 37^{\circ}} = \frac{2 \times 10 \times 3 / 5}{10 \times 4 / 5} = 1.5 s \\ R = (v_{0} \cos 37^{\circ}) T + \frac{1}{2} (g \sin 37^{\circ}) T^{2} \end{array}$
For cart:
$R - 6 = v T + \frac{1}{2} (g \sin 37^{\circ}) T^{2}$
Solve the equations to get v = 4 m/s

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