a catapult launches a pumpkin at 80m/s at 60 degrees above the horizontal.what horizontal distance will it travel?

Question

A physics question involving resolving motion vectors

Answer 1

Break this problem into two parts, vx and vy, and sx and sy.

vx = 80 m/s * cos(60 degrees) = 80 m/s * 1/2 = 40 m/s

vy = 80 m/s * sin(60 degrees) = 80 m/s * sqrt(3) / 2 = 40 m/s * sqrt(3)

vy = 69.28 m/s

at an acceleration of -9.81 m/s^2, it will take about 7 s for the pumpkin to reach its maximum height (because it's slowing down about 10 m/s every second).

t = 69.28 m/s / 9.81 s

t_to_reach_peak = 7.062 s

The pumpkin takes the same time to fall from its max height to the ground

t_to_fall = 7.062 s

t_in_air = 2 * 7.062 s = 14.124 s

The pumpkin is traveling horizontally at 40 m/s every second.

There is no horizontal force, so there is no horizontal acceleration, so vx = constant

sx = 40 m/s * 14.124 s = 564.96 m

sx = 570 m (to 2 significant digits, if we assume 80 = 80., and 60 = 60.)

the pumpkin will travel 570 m through the air, this is the answer