Question

If a ball that is 10 meters above the ground is thrown horizontally at 5.51 meters per second. a. how long will it take for the ball to hit the ground? b. how far will the ball travel in the horizontal direction before it hits the ground?​

Answer 1

a. t = 1.43 s

b. d = 7.88 m

Step-by-step explanation:

a. The time of flight can be found using the following equation:

`y_(f) = y_(0) + v_{0_(y)}t - (1)/(2)gt^(2)`

Where:

`y_(f)`: is the final height = -10 m

`y_(0)`: is the initial height = 0

`v_{0_(y)}`: is the initial speed in the vertical direction = 0

g: is the acceleration due to gravity = 9.81 m/s²

By solving the above equation for "t" we have:

`t = \sqrt{(2y_(f))/(g)} = \sqrt{(2*10 m)/(9.81 m/s^(2))} = 1.43 s`

Hence, the ball will hit the ground in 1.43 s.

b. The distance in the horizontal direction can be found as follows:

`x_(f) = x_(0) + v_(0)t + (1)/(2)at^(2)`

Where:

x₀: is the initial position in the horizontal direction = 0

a: is the acceleration in the horizontal direction = 0 (it is moving at constant speed)

`x_(f) = 5.51 m/s*1.43 s = 7.88 m`

Therefore, the ball will travel 7.88 m before it hits the ground.

I hope it helps you!