8. A pitcher throws a baseball off a 20m high cliff into a canyon at 30degrees above the horizon at an initial velocity of 35m/s. How far will the ball travel horizontally from the pitcher? Assume no air resistance.

9. How high will the ball get from the bottom of a canyon?
10. How fast will the ball be moving when it hits the ground?

vertical velocity initial: 20sin30=10m/s

time in air:
hf=hi+10*t-4.9t^2
0=20+10t-4.9t^2 solve for t, time in air.
horizonal distance= 20cos30*t

how high? at the top, v is zero in the vertical, 0=10-9.8t solve for time to top, t hf=20+10t-4.9t^2 solve for hf

how fast?
use the time in air t,
vf=20t-9.8t^2

oops, on how fast

vf=20-9.8t

To find the answers to these questions, we can use the equations of motion for projectile motion. Projectile motion involves the motion of an object that is launched into the air and moves along a curved path under the influence of gravity.

Let's break down each question and step through the process of finding the answers:

8. How far will the ball travel horizontally from the pitcher?

To find the horizontal distance traveled by the ball, we need to consider the time of flight and the horizontal component of the initial velocity. The time of flight can be calculated using the formula:

Time of flight = (2 * initial velocity * sin(angle))/acceleration due to gravity

In this case, the initial velocity is 35m/s and the angle above the horizon is 30 degrees (which we need to convert to radians). The acceleration due to gravity is approximately 9.8 m/s^2.

So, first, let's convert the angle to radians:

angle in radians = angle in degrees * (pi/180)
angle in radians = 30 * (pi/180)
angle in radians = pi/6

Now, we can calculate the time of flight:

Time of flight = (2 * 35 * sin(pi/6))/9.8

Next, use the value of the time of flight to find the horizontal distance traveled:

Horizontal distance = initial velocity * cos(angle) * time of flight

Horizontal distance = 35 * cos(pi/6) * (2 * 35 * sin(pi/6))/9.8

Simplify the equation to find the answer.

9. How high will the ball get from the bottom of a canyon?

To find the maximum height reached by the ball, we can use the formula for the vertical displacement:

Vertical displacement = (initial velocity * sin(angle))^2 / (2 * acceleration due to gravity)

Using the values given in the question, plug them into the equation to find the answer.

10. How fast will the ball be moving when it hits the ground?

To find the final velocity of the ball when it hits the ground, we can use the formula:

Final velocity = initial velocity + (acceleration due to gravity * time of flight)

Substitute the values into the equation to calculate the final velocity.