Question

Consider a pitcher throwing a ball. If he is on a tower so that the ball is 5m off the ground when thrown horizontally, and the ball lands 18m downrange, what is the speed of the ball?

Answer 1

someone please help me

Answer 2

@ganeshie8

Answer 3

@freckles

Answer 4

You need two steps to get to the solution.

Step #1: calculate the time taken for the ball to hit the ground
This is only dependent on the vertical motion of the ball. So you can find the time by assuming the ball is just falling under the influence of gravity:\[h = \frac{1}{2}gt^{2}\]
Step #2: calculate the horizontal speed of the ball
By understanding that with no air resistance the ball will move at the same velocity for its flight, you can write that its distance traveled is simply the product of velocity and time.\[x = vt\]

Answer 5

El

Answer 6

is the equation to find t this one t= sqrt(.5*g)/h

Answer 7

@Abhisar can you help me real quick

Answer 8

okay

Answer 9

so do i use Pythagorean theoream?

Answer 10

Wait.. (-:

Answer 11

ok, You need to find out the horizontal speed by which the ball was thrown..right?

Answer 12

yes

Answer 13

So to find that we would have to first find out the time of flight of the ball.

Answer 14

yes

Answer 15

The ball when thrown had two motions, one in the horizontal direction and second in the vertical direction. We can find out the time by using its vertical motion.

We can use the equation \(\tt S=ut+\frac{1}{2}a\times t^2\) to find out the time.

Answer 16

Calculate the time, what would it be?

Answer 17

is that a kinematic equation?

Answer 18

Yes (-:

Answer 19

so we need the t on the left side right/

Answer 20

\(\huge \checkmark\)

Answer 21

would it be t=1/2a / s-u?

Answer 22

Just plug in the values, s will be 5, u will be 0 since ball was thrown horizontally and a will be 10 (acceleration due to gravity).

Answer 23

So, the equation will be like

\(\tt 5 = 0\times t + \frac{1}{2}\times 10\times t^2\), find t

Answer 24

t = sqrt(1/5)

Answer 25

Nopes.....

Answer 26

oh crap forgot the 1/2 its sqrt of 1

Answer 27

right?

Answer 28

\(\huge \checkmark\)

Answer 29

Now the second and final part comes in. You can use the same equation to calculate the horizontal speed.

This time we will consider ball's horizontal motion.
Take s=18, t= 1 and a=0 (there is no horizontal acceleration). Plugging in the values we get,

\(\tt 18 = u\times 1+\frac{1}{2}\times 0 \times 1^2\), find the value of u

Answer 30

u= 18

Answer 31

right?

Answer 32

\(\huge \checkmark\)

Answer 33

That's the answer (-:

Answer 34

thank you so much

Answer 35

Welcome (-: