Question

You are standing on your back porch which is 2.4 m above your backyard. you throw a ball horizontally for your dog to chase and it goes a distance of 14 m, landing in the backyard below. what is the initial horizontal velocity of the ball when you threw it?

Answer 1

The initial horizontal velocity of the ball when thrown is 28.46 m/s.

Step-by-step explanation:

To find the initial horizontal velocity of the ball, we can use the equation for horizontal motion:

vx = d / t

where vx is the initial horizontal velocity, d is the horizontal distance traveled (14 m), and t is the time of flight.

However, since the ball was thrown horizontally, the vertical component of the initial velocity is zero. Therefore, the time of flight can be found using the equation for vertical motion:

y = v0y * t + (1/2) * g * t^2

where y is the vertical displacement (the height of the porch, 2.4 m), v0y is the initial vertical velocity, and g is the acceleration due to gravity (-9.8 m/s^2).

Since the ball is thrown horizontally, the initial vertical velocity v0y is zero. Solving for t in the vertical motion equation, we get:

t = sqrt((2 * y) / g)

Substituting the known values, we have:

t = sqrt((2 * 2.4) / 9.8) = 0.492 s

Finally, substituting the values of t and d into the horizontal motion equation, we can solve for vx:

vx = d / t = 14 m / 0.492 s = 28.46 m/s