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 horizontal distance traveled by the cannonball before hitting the ground can be calculated using the formula:
Range = (initial velocity^2 * sin(2*angle)) / g
A2. The maximum height reached by the cannonball can be calculated using the formula:
Max height = (initial velocity^2 * (sin(angle))^2) / (2*g)
B. The maximum height reached by the cannonball as observed by an observer at the bottom of the cliff would be the same as the maximum height calculated in A2.
C. The horizontal distance traveled by the cannonball before hitting the ground can be calculated using the same formula as in A1.
D. The time taken for the cannonball to hit the ground can be calculated using the formula:
Time of flight = (2 * initial velocity * sin(angle)) / g
26. The formula to solve for the range of a projectile is:
Range = (initial velocity^2 * sin(2*angle)) / g
27. To solve for the release angle, you can rearrange the formula for range to solve for the angle:
angle = 1/2 * arcsin((g * Range)/(initial velocity^2))