Problem Solving: Read and analyze each problem carefully and answer the succeeding questions. Write your solution legibly and box
your final answer. Each problem is worth five points.
21-25. A cannon is fired from the top of a cliff that is 50 meters high above the ground. The cannonball is launched with an initial velocity
of 80 m/s at 30-degrees angle above the horizontal. (Ignoring air resistance)
A.
What is the formula to solve for:
A1. The horizontal distance traveled by the cannonball before hitting the ground.
A2. The maximum height reached by the cannonball.
B.
What is the maximum height reached by the cannonball as observed by an observer at the bottom of the cliff?
C.
What is the horizontal distance traveled by the cannonball before hitting the ground?
D.
How much time does it take for the cannonball to hit the ground?
26-30. A golf player was standing 20 meters away from the cup. If the golf player could hit the golf ball, releasing it with an initial speed
of 15 m/s, what would be the release angle to ensure that the ball will shoot to the cup (this where the ball needs to land)? Ignore air
resistance.
A. What is the formula to solve for the range of a projectile?
B.
Solve for the release angle.
A1. The formula to solve for the horizontal distance traveled by the cannonball before hitting the ground is:
Range = (initial velocity^2 * sin(2*launch angle)) / g
where:
- initial velocity = 80 m/s
- launch angle = 30 degrees
- g = acceleration due to gravity = 9.8 m/s^2
A2. The formula to solve for the maximum height reached by the cannonball is:
Height = (initial velocity^2 * (sin(launch angle))^2) / (2*g)
B. The maximum height reached by the cannonball as observed by an observer at the bottom of the cliff is the same as the height mentioned in part A2, which is solved using the formula provided.
C. To solve for the horizontal distance traveled by the cannonball before hitting the ground, use the formula provided in part A1. Calculate the distance using the given values.
D. To calculate the time it takes for the cannonball to hit the ground, you can use the formula for projectile motion:
Time = (2 * initial velocity * sin(launch angle)) / g
Substitute the given values to find the time taken.
For problem 26-30:
A. The formula to solve for the range of a projectile is:
Range = (initial velocity^2 * sin(2*launch angle)) / g
B. To solve for the release angle that ensures the ball shoots into the cup, you can rearrange the range formula and solve for the launch angle. Given the initial velocity and distance from the cup, find the launch angle that will give you the desired range.