Question

A ball is fired from the ground with an initial speed of 1.70 x 103 m/s (approximately five times the speed of sound) at an initial angle of 55.0° to the horizontal. Neglecting air resistance, find
a. the ball’s horizontal range.
b. the amount of time the ball is in motion

Answer 1

I think you mean initial speed =1.70 * 10^3 m/s
Vertical problem:
Vi = 1.70 * 10^3 sin 55 = 1.39 * 10^3
v = Vi - g t
at top v = 0
t at top = 1.39*10^3 / 9.81 = 1.5 * 10^2 seconds upward ( so total time in air = 300 seconds)
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Horizontal problem:
u = 1700 cos 55 = 975 m/s
for 300 seconds so range = 975*300 = 292500 meters = 293 km

Answer 2

By the way anything shaped like a ball would burn up at that speed.