8. A cyclist is coasting at 14 m/s when she starts down a 460 m long slope that

Question

8. A cyclist is coasting at 14 m/s when she starts down a 460 m long slope that is 30 m high. The cyclist and her bicycle have a combined mass of70 kg. A steady 15 N drag force due to air resistance acts on her as she coasts all the way to the bottom.

question:What is her speed at the bottom of the slope?

7.Your friend's Frisbee has become stuck 27 mabove the ground in a tree. You want to dislodge the Frisbee by throwing a rock at it. The Frisbee is stuck pretty tight, so you figure the rock needs to be traveling at least 5.1 m/s when it hits the Frisbee.

question : If you release the rock 1.7 m above the ground, with what minimum speed must you throw it?

Explanation / Answer

solution:

8)

= arcsin(30/460) = 3.74º
weight downslope = mgsin = 70kg * 9.8m/s² * sin3.74 = 44.74 N
friction upslope = 15 N
net downslope force = 44.74-15N =29.74 N

net downslope acceleration = 29.74N / 70kg = 0.425 m/s²
Now use Torricelli's equation:
v² = u² + 2as = (14m/s)² + 2 * 0.425m/s² * 460m = 586.85 m²/s²
v = 24.23 m/s ans

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