A golf ball (m=0.46g is struck by a club on a 50 deg. angle over 7ms. If the bll lands 200 m away, what is the force delivered to it by the club

To determine the force delivered to the golf ball by the club, we can use the principles of projectile motion and Newton's second law of motion.

Step 1: Find the initial velocity of the golf ball.
Given that the golf ball was struck at an angle of 50 degrees, we can decompose the initial velocity into horizontal and vertical components. The vertical component of the velocity can be found using the formula: Vy = V * sin(θ), where V is the initial velocity and θ is the angle of projection. Plugging in the values, we get Vy = V * sin(50).

Step 2: Find the initial vertical velocity of the golf ball.
The initial vertical velocity can be found using the formula: Vy = V * cos(θ), where V is the initial velocity and θ is the angle of projection. Plugging in the values, we get Vx = V * cos(50).

Step 3: Find the time of flight.
The time of flight can be calculated using the formula: t = 2 * Vy / g, where g is the acceleration due to gravity. Plugging in the values, we get t = 2 * Vy / g.

Step 4: Find the horizontal distance traveled by the golf ball.
The horizontal distance can be calculated using the formula: Dx = Vx * t. Plugging in the values, we get Dx = Vx * t.

Step 5: Calculate the force delivered by the club.
Using Newton's second law of motion, we know that force (F) equals mass (m) multiplied by acceleration (a). The acceleration can be calculated using the formula: a = ΔV / t, where ΔV is the change in velocity. Plugging in the values, we get a = ΔV / t. Given that the initial velocity is V and the final velocity is 0, ΔV = V. Thus, a = (V - 0) / t = V / t.

Finally, F = m * a.

Now, let's substitute the given values into these equations and solve for the force:

Given values:
m (mass) = 0.46 g = 0.00046 kg
V (initial velocity) = ?
θ (angle of projection) = 50 degrees
g (acceleration due to gravity) = 9.8 m/s^2
Dx (horizontal distance traveled) = 200 m
t (time of flight) = 7 ms = 0.007 s

By solving the equations above, we can find the force delivered to the golf ball by the club.