A pumpkin, here on Earth, becomes a projectile in being hurled from a large slin

Question

A pumpkin, here on Earth, becomes a projectile in being hurled from a large sling shot. It lands 240 m from the sling shot after 6 seconds. Take g-10 m/s2. Assume it lands at the same height it was shot at. Determine the initial horizontal velocity component of the pumpkin. The initial velocity here, and below, is the velocity upon just leaving the sling shot. Therefore, the initial velocity is clearly not zero. Determine the speed of the pumpkin at its maximum height. If it takes 3 seconds to reach its maximum height, determine the vertical component of the initial velocity of the pumpkin. Determine the initial speed of the pumpkin. a. b. c. d.

Explanation / Answer

given,

horizontal distance = 240 m

time = 6 sec

since there is no horizontal force

horizontal velocity = horizontal distance / time

horizontal velocity = 240 / 6

horizontal velocity = 40 m/s

at maximum height vertical velocity is 0, so all is left is horizontal velocity

speed at maximum height = 40 m/s

by first equation of motion

v = u + gt

0 = u - 10 * 3

u = 30 m/s

initial vertical velocity = 30 m/s

initial speed = sqrt(vertical speed^2 + horizontal speed^2)

initial speed = sqrt(30^2 + 40^2)

initial speed = 50 m/s

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