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.
Please answer it correctly and put a step by step solutions
21.
A1. The horizontal distance traveled by the cannonball before hitting the ground can be solved using the range formula:
Range = (initial velocity)^2 * sin(2*angle) / acceleration due to gravity
A2. The maximum height reached by the cannonball can be solved using the following formula:
Maximum height = (initial velocity*sin(angle))^2 / (2*acceleration due to gravity)
B. To find the maximum height reached by the cannonball as observed by an observer at the bottom of the cliff, you need to add the height of the cliff to the maximum height reached.
C. The horizontal distance traveled by the cannonball before hitting the ground can be determined by plugging in the values to the range formula.
D. To find how much time it takes for the cannonball to hit the ground, you can use the time of flight formula:
Time = (2*initial velocity*sin(angle)) / acceleration due to gravity
26.
A. The formula to solve for the range of a projectile is:
Range = (initial velocity)^2 * sin(2*angle) / acceleration due to gravity
B. To solve for the release angle, you need to find the angle that maximizes the range. This can be done by differentiating the range formula with respect to the angle, setting it equal to zero, and solving for the angle.
Make sure to show all calculations and step-by-step solutions for full credit. Box your final answers for each part of the problem.