Question

A baseball leaves the bat with a speed of 40 m/s at an angle of 35 degrees. A 12m tall fence is placed 130 m from the point the ball was struck. Assuming the batter hit the ball 1m above ground level, does the ball go over the fence? If not, how does the ball hit the fence? If yes, how far beyond the fence does the ball land?

Answer 1

The ball land at 3.00 m.

Step-by-step explanation:

Given that,

Speed = 40 m/s

Angle = 35°

Height h = 1 m

Height of fence h'= 12 m

We need to calculate the horizontal velocity

Using formula of horizontal velocity

`V_(x)=V_(i)\cos\theta`

`V_(x)=40*\cos35`

`V_(x)=32.76\ m/s`

We need to calculate the time

Using formula of time

`t = (d)/(v)`

`t=(130)/(32.76)`

`t=3.96\ sec`

We need to calculate the vertical velocity

`v_(y)=v_(y)\sin\theta`

`v_(y)=40*\sin35`

`v_(y)=22.94\ m/s`

We need to calculate the vertical position

Using formula of distance

`y(t)=y_(0)+V_(i)t+(1)/(2)gt^2`

Put the value into the formula

`y(3.96)=1+22.94*3.96+(1)/(2)*(-9.8)*(3.96)^2`

`y(3.96)=15.00\ m`

We need to calculate the distance

`s = y-h'`

`s=15.00-12`

`s=3.00\ m`

Hence, The ball land at 3.00 m.