A volleyball is spiked over the net at an angle of 65° below the horizontal with a horizontal acceleration of 1.7 m/s. What is the vertical force of the ball if it weighs 27 N?

Answer 1

Assuming you meant the acceleration was 1.7 m/s², you could draw a sketch like this:

Using the triangle in the upper right, you can use the following trig ratio to solve for a_y:

tan(65°) = a_y/1.7

a_y = 1.7tan(65°) = 3.646 m/s²

Since the weight of the ball is 27 N, we can calculate its mass using W = mg or m = W/g = 27/9.8 = 2.76 kg

Since F = ma then the vertical force due to the spike is:

F = (2.76)(3.646) = 10.04 N

But, the ball already has an acceleration due to gravity and so that needs to be added in. That acceleration force is the 27 N. So the total vertical force is F_total = F_spike + F_gravity = 37 N (rounded to 2 sig figs)