Question

A slingshot fires a pebble from the top of a building at a speed of 13.0 m/s. The building is 22.0 m tall. Ignoring air resistance, find the speed with which the pebble strikes the ground when the pebble is fired (a) horizontally, (b) vertically straight up, and (c) vertically straight down.

Answer 1

For an object in free fall, the final velocity (Vf) can be calculated using the equation:
Vf = sqrt(Vi^2 + 2g*d), where
Vi = initial velocity (13 m/s)
g = acceleration due to gravity (9.8 m/s^2)
d = change in vertical position (22 m)

(a) Horizontally: The pebble does not fall, so its velocity does not change, thus Vf = 13 m/s.

(b) Vertically straight up: The change in vertical position (d) is positive, so the final velocity will be less than the initial velocity.
Vf = sqrt(13^2 + 2 * 9.8 * 22) = sqrt(13^2 + 437.6) = sqrt(437.6 + 169) = sqrt(606.6) = 24.7 m/s

(c) Vertically straight down: The change in vertical position (d) is negative, so the final velocity will be greater than the initial velocity.
Vf = sqrt(13^2 - 2 * 9.8 * 22) = sqrt(13^2 - 437.6) = sqrt(169 - 437.6) = sqrt(-268.6) = not defined (velocity is imaginary)

I did not have paper so I may have got a couple things wrong .