A daredevil rides a go-cart, first down a hill and then she makes a jump using a

Question

A daredevil rides a go-cart, first down a hill and then she makes a jump using a ramp (as depicted above). The ramp makes a 30 degree angle with respect to the horizontal. The hill has an elevation of h_i = 900 m high. Take the mass of the go-cart plus daredevil to be 200 kg. (Assume that the go-cart does not provide any acceleration and that there is no friction or air resistance, thus the only relevant force in the problem is gravity.) (a) Determine the daredevil's kinetic energy at the ramp. (b) Write the x and y components of the daredevil's velocity at the ramp. (c) Determine how high the daredevil goes during her jump (find h).

Explanation / Answer

(a) form conservation of energy, we have

K = U = m g h = 200 x 10 x 900 =1.8 X 106 J

(b)

The velocity is,

K =1/2 m v2

1.8 X 106 J = (1/2 ) (200) v2

v = 134 m/s

x component of velocity:

vx = vcos30 = 134 cos 30 = 116 m/s

y component of velocity:

vy = vsin30 = 134 sin30 = 67 m/s

(c)

maximum height: hmax = u2/2g

= (67)2 / 2 (10)

= 224.45 m

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