A ball is thrown horizontally from the top of a 55 m building and lands 150 m from the base of the building. Ignore air resistance, and use a coordinate system whose origin is at the top of the building, with positive y upwards and positive x in the direction of the throw.

a) t = 3.349 s

b) V_x, i = 44.8 m/s

c) V_y, f = 32.85 m/s

d) V = 55.55 m/s

Explanation:

Given:

- Total throw in x direction x (f) = 150 m

- Total distance traveled down y (f) = 55 m

Find:

a) How long is the rock in the air in seconds.

b) What must have been the initial horizontal component of the velocity, in meters per second?

c) What is the vertical component of the velocity just before the rock hits the ground, in meters per second?

d) What is the magnitude of the velocity of the rock just before it hits the ground, in meters per second?

Solution:

- Use the second equation of motion in y direction:

y (f) = y (0) + V_y, i*t + 0.5*g*t^2

- V_y, i = 0 (horizontal throw)

55 = 0 + 0 + 0.5 * (9.81) * t^2

t = sqrt (55 * 2 / 9.81)

t = 3.349 s

- Use the second equation of motion in x direction:

x (f) = x (0) + V_x, i*t

150 = 0 + V_x, i*3.349

V_x, i = 150 / 3.349 = 44.8 m/s

- Use the first equation of motion in y direction:

V_y, f = V_y, i + g*t

V_y, f = 0 + 9.81*3.349

V_y, f = 32.85 m/s

- The magnitude of velocity of ball when it hits the ground is:

V^2 = V_y, f^2 + V_x, i^2

V = sqrt (32.85^2 + 44.8^2)

V = 55.55 m/s