projectile motion in phys

Question

Brett hits a 0.06 kg golf ball directly toward flagstick from a point 238 meters away. The velocity of the ball as it leaves the golf club is 45 m/s at angle of 40 degrees to the horizontal The flagstick is in the hole at the same level as the tee box where the ball is initially at rest (there is no net change in vertical height). The ball is in contact with the club for 0.05 seconds. Ignore air resistance during the flight of the golf ball.

a)Calculate the magnitude of the average net force exerted on the ball from the golf club.

b)Calculate the time the golf ball is in the air when it hits the level ground near the flagstick.

c)Calculate the distance from the flagstick to the golf ball when it hit the ground. Did the ball hit ground before or after the flagstick?

d)Calculate the maximum height of the golf ball.

Answer 1

Newton's second law: F = ma

Definition of acceleration: a = (v - v_o)/t

m = 0.06 kg

t = 0.05 s

v = 45 m/s

v_o = 0

Θ = 40^o

Part a) we are given the mass, change in velocity, and time the club was in contact with the ball. The force of the club:

F = ma

F = m (v-v_o)/t

= (0.06kg)(45m/s)/0.05s)

= (0.06)(45)/0.05 kg*m/s².(Newton)

b) The time the ball is in the air is only affected by gravitational acceleration, thus use only the 'y direction' to determine time of flight. Remember total time = t_up + t_down . Since there isn't any air resistance, t_up = t_down . Solve for t_up using kinematic equations. Hint: what is v_final for the trip 'up'? *** use only the 'y' component of the initial velocity *** Use a triangle and trig relations with the velocity vector on the diagonal at an angle of 40⁰ with the horizontal to find v_y - the vertical component- (and v_x - the horizontal component- for part d) . Use only sine and cosine.

c) Given that the flagstick is 238 m away from the initial position of the ball, we need to calculate the total distance in the 'x direction' for the horizontal distance traveled by the golf ball. Using total time and v_x from above, and the definition of velocity (v = d/t), we can determine the distance traveled (d = v*t) . Compare it to the distance given for the flagstick before the initial hit to determine where the ball landed with respect to the flagstick.

d) To determine the height the ball travels, we need the time calculated from part b. Only the time going up since we want total height. Use that with the other information and the kinematic equations to solve for height. (Using t_up from part a and v_y from part b.)