1. A truck, initially at rest, rolls conservatively down a hill of height h and
ID: 1384676 • Letter: 1
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1. A truck, initially at rest, rolls conservatively down a hill of height h and attains a speed of 6.0 m/s at the bottom. If the truck then rolls conservatively down a hill that is at height 9h what will its speed be at the bottom? (a) 9.0 m/s (b) 12 m/s (c) 15 m/s (d) 18 m/s (e) 24 m/s 2. A cart starting from rest rolls down a hill. At the bottom it attains a speed of 8.5 m/s. If the cart were given an initial push, so its initial speed at the top of the hill is 8.5 m/s, what will its speed be at the bottom (assume the system is conservative)? (a) 8.5 m/s (b) 12 m/s (C) 17.0 m/s (d) 24.5 m/s (e) 36 m/s 3. A 68.-kg surfer starts at the top of a wave at v = 1.5 m/s, drops a distance of 12 m (40 ft) to end with a speed of 23 m/s (52 mph). How much work was done on the surfer by the wave (show your work)? (*BONUS* What constant acceleration would get the surfer up to his final speed if his ride during the drop is actually 31 m?) 4. Two PasCars are at rest nose-to-nose. The red Pascar is 255 g, and the blue Pascar is 555 g. The spring gun of the red Pascar is fired giving a conservative horizontal push of 12.5 N for 0.150 s to the blue Pascar. What is the magnitude of the final speed and momentum of each Pascar (show your work ?Explanation / Answer
1. conserve energy , mgh = 1/2mv2 + 1/2mk2 v2/R2
so, 2gh = v2( 1 + (k/R)2
Again 18gh = v12( 1 + (k/R)2
Divide second eqn by first, we get . 3 = v1/6
So, V1= 18m/s.
2. mgh = 1/2 mv2
second condition, mgh + K1=K2
2mgh = 1/2 mv2
So, V2 = 4gh
So new speed = 12m/s
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