she hit the ball downward? at -4.00° ?
very unusual serve!
fix that, find the time of flight (t when h(t)=0)
the horizontal speed is constant, so see how far it went
(you might check to make sure that the ball actually cleared the net)
Canadian star tennis player Bianca Andreescu defeated Serena Williams in the 2019 US Open tournament. During the match Bianca served an ace right up the middle of the court. The ball left her racket 2.58 m above the court with a speed of 50.1 m/s and at an angle of -4.00o. On a tennis court, the net is 11.6 m along the ground from where the ball is served and is 0.914 m high. How far from the net did the ball land on the other side??
4 answers
well, let's assume it got over the net, where will it hit the turf?
Vertical problem
a = -g = -9.81 m/s^2
v = Vi - 9.81 t = -50.1 sin 4 deg - 9.81 t = -5.49 - 9.81 t
h = Hi + Vi t - 4.9 t^2 = 2.58 - 5.49 t - 4.9 t^2
solve quadratic for h = 0
4.9 t^2 + 5.49 t - 2.58 = 0
t = use the positive t, not the negative one for on the way up:)
then horizontal problem
u = constant horizontal speed = 50.1 cos 4 deg
distance from racquet to where ball hits ground = u t
subtract 11.6 meters from that for distance beyond the net
Vertical problem
a = -g = -9.81 m/s^2
v = Vi - 9.81 t = -50.1 sin 4 deg - 9.81 t = -5.49 - 9.81 t
h = Hi + Vi t - 4.9 t^2 = 2.58 - 5.49 t - 4.9 t^2
solve quadratic for h = 0
4.9 t^2 + 5.49 t - 2.58 = 0
t = use the positive t, not the negative one for on the way up:)
then horizontal problem
u = constant horizontal speed = 50.1 cos 4 deg
distance from racquet to where ball hits ground = u t
subtract 11.6 meters from that for distance beyond the net
I am not sure 4 degrees downward is unusual. The racquet is high at contact and the speed is scary.
I get t = 0.356 second
distance from server = 0.998 * 50.1 * 0.356 = 17.8 meters
subtract 11.6
6.19 meters beyond the net
distance from server = 0.998 * 50.1 * 0.356 = 17.8 meters
subtract 11.6
6.19 meters beyond the net