A farm truk moves due north with a constant velocity of 9.50 m/s on a limitless

Question

A farm truk moves due north with a constant velocity of 9.50 m/s on a limitless horizontal streach 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 16.0 m farther down the road.(a) In the farme 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) what shape of can's trajectory as seen by  the boy? (d)An observer on the ground watches the boy throw the can and catch it. in this observer's ground frame of reference, describe the shap of the can's path and determine the initial velocity of the can.

Explanation / Answer

c) The shape of the trajectory is straight up and backdown. This has been told to you as he catches at the samespot (relative to the truck) as he threw it.
d) an observer on the ground will see a parabola. It will rise the same height as seen by the boy on the truck,but it travels forward 16 meters from where it was thrown. Todetermin the intial velocity. let's first find the time. Thetrajectory can be written as x and y parametric equations, x(t) isa constant, the same as the truck velocity. So, the time thecan is in the air is then 16/9.5 = 1.68 seconds. The yequation is y = 1/2 at2 + v0t + y0. The last term is zero ifwe call the height of the truck bed 0. So y(t) = 1/2 (-9.8)(t2) +v0t. At t = 1.68, y = 0. So 0 = -13.9 + 1.68 v0. So, the initial y velocity is 8.25 m/sec. The groundobserver will see the intial velocity as the combination of the twovectors, x at 9.5m/sec and y at 8.25 m/sec. These vectors addas sqrt( sum of squares) which is 12.58 m/sec. It wasn'tasked, but the angle is tan-1 (8.25/9.5).
The answers to a and b are in the above description, providedif you follwed it.

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