1. A water-skier lets go of the tow rope upon leaving the end of a jump ramp at 14 m/s. The skier has a speed of 13 m/s at the highest point of the jump. Ignoring air resistance, determine the skier's height above the top of the ramp at the highest point.
2. A motorcycle (mass of cycle plus rider = 250 kg) is travelling at a steady speed of 20 m/s. The force of air resistance acting on the cycle and rider is 200 N. Find the power necessary to sustain this speed if (a) the road is level, and (b) the road is sloping upward at 37 degrees with respect to horizontal.
I have been giving the answers (1. 1.38 m 2. (a) 4 kW (b) 33 489 W) but I can't figure out how to get to the answers. If you could show me working I would be very grateful. :)
2. A motorcycle (mass of cycle plus rider = 250 kg) is travelling at a steady speed of 20 m/s. The force of air resistance acting on the cycle and rider is 200 N. Find the power necessary to sustain this speed if (a) the road is level, and (b) the road is sloping upward at 37 degrees with respect to horizontal.
I have been giving the answers (1. 1.38 m 2. (a) 4 kW (b) 33 489 W) but I can't figure out how to get to the answers. If you could show me working I would be very grateful. :)
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(1).
V² = Vx² + Vy²
14² = 13² + Vy²
Vy² = 14² - 13²
v² = Vy² + 2 g h
0² = (14² - 13²) + 2 (-9.8) h
h = 1.37755 m
(2a).
ΣF = 0
F - f = 0
F - 200 = 0
F = 200 N
P = F v
P = 200(20)
P = 4000 watt
(2b).
ΣF = 0
F - f - mg sin 37 = 0
F - 200 - (250)(9.8) sin 37 = 0
F = 1674.45 Newton
P = F v
P = (1674.45)(20)
P = 33489 watt
V² = Vx² + Vy²
14² = 13² + Vy²
Vy² = 14² - 13²
v² = Vy² + 2 g h
0² = (14² - 13²) + 2 (-9.8) h
h = 1.37755 m
(2a).
ΣF = 0
F - f = 0
F - 200 = 0
F = 200 N
P = F v
P = 200(20)
P = 4000 watt
(2b).
ΣF = 0
F - f - mg sin 37 = 0
F - 200 - (250)(9.8) sin 37 = 0
F = 1674.45 Newton
P = F v
P = (1674.45)(20)
P = 33489 watt