A farm truck moves due east with a constant velocity of 11.50 m/s on a limitless

Question

A farm truck moves due east with a constant velocity of 11.50 m/s on a limitless horizontal stretch of road. A boy riding on the back of the truck throws a can of soda upward and catches the projectile at the same location on the truck bed, but 17.0 m farther down the road.

(a) In the frame of reference of the truck, at what angle to the vertical does the boy throw the can?
(b) What is the initial speed of the can relative to the truck?
(c) In this observer's frame of reference, determine the initial velocity of the can.
magnitude AND direction: _____° above the horizontal

Explanation / Answer

We can find the time of flight of the can by considering its horizontal motion: x = xo+ vot + (0.5)at^2 17m = (11.5 m/s) t + 0 t = 1.478 s (a) For the boy to catch the can at the same location on the truck bed, he must throw it straight up, at 0° to the vertical. (b) For the free fall of the can, yf = yi + vyit + (1/2)ayt2: 0 = 0 + vyi (1.478 s) - (1/2)(9.8 m/s2)(1.478 s)2 vyi= 7.24 m/s (c) The boy sees the can always over his head, traversing a straight line segment upward and then downward. (d) The ground observer sees the can move as a projectile on a symmetric section of a parabola opening downward. Its initial velocity is: v o=v(11.5^2+ 7.24^2) = 13.5 m/s north at tan-1(7.24/11.5) = 32° above the horizontal

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