# A cannon barrel is elevated at an angle of 45°. It fires a ball with a speed of 250 m/s. (For the following questions, ignore air resistance.)

(a) What height does the ball reach?

m

(b) How long is the ball in the air?

s

(c) What is the horizontal range of the cannon?

kmp

## h=vvertical*time-1/2 g t^2

h=0=250*.707*t-4.0t^2

t= 250*.707/4.9 seconds

range: 250cos45*timeinair.

## To solve these questions, we can use the principles of projectile motion. In projectile motion, we can break down the motion into horizontal and vertical components.

(a) To find the height the ball reaches, we need to determine the vertical displacement. We can use the equation:

displacement = (initial velocity * time) + (0.5 * acceleration * time^2)

Since the ball is fired vertically upwards, the final displacement is zero. The acceleration is the acceleration due to gravity (-9.8 m/s^2), and the initial velocity is the vertical component of the initial velocity, which can be found using:

vertical velocity = initial velocity * sin(theta)

where theta is the angle of elevation.

So, for part (a):

Find the vertical displacement by plugging in the values into the equation above.

(b) To find the time the ball is in the air, we can use the vertical motion equation:

final velocity = initial velocity + (acceleration * time)

Since the final velocity is zero when the ball reaches its maximum height, we can solve for time using:

0 = initial velocity + (acceleration * time)

So, for part (b):

Solve for time by plugging in the values into the equation above.

(c) To find the horizontal range of the cannon, we need to determine the horizontal displacement. We can use the equation:

displacement = (initial velocity * time) + (0.5 * acceleration * time^2)

Since the horizontal velocity remains constant throughout the motion, the initial and final velocities are the same. The initial velocity is the horizontal component of the initial velocity, which can be found using:

horizontal velocity = initial velocity * cos(theta)

where theta is the angle of elevation.

So, for part (c):

Find the horizontal displacement by plugging in the values into the equation above. To convert the answer to kilometers, divide the result by 1000.

By following these steps and calculations, you will be able to find the answers to the given questions.