An arrow toward a 300-g target that is sliding in her direction at a speed of on

Question

An arrow toward a 300-g target that is sliding in her direction at a speed of on a smooth, slippery surface. The 22.5-g arrow is shot with 36.0 m/s and through the target, which is stopped by the impact. What is the speed of the arrow after passing through the target? Gayle runs at a speed of 4.30 m/s amd dives on a sled, initially at rest on the top of a frictionless crow-covered hill. After she has descended a vertical distances of 5.00 m, her brother, who is initially at test, hops on her back and together they continue down the hill. What is their speed at the bottom of the hill at the total vertical drop is 15.0 m? Gayle's mass is 48.0 kg, the sled has a mass of 5.50 kg and her brother has a mass of 30.0 kg.

Explanation / Answer

here,

initial speed of gayle , u = 4.3 m/s

mass of gayle , mg = 48 kg

sled mass , ms = 5.5 kg

let the speed of Gayle and sled be vgs = mg * u/(ms + mg)

vgs = 3.86 m/s

mass of her brother , mb = 30 kg

at verticl drop of h = 5 m , let the speed of gayle be u'

using conservation of energy

0.5 * (mg + ms) * u'^2 - 0.5 * (mg + ms) * vgs^2 = (mg + ms )*g*h

u'^2 - 3.86^2 = 2 * 9.8 * 5

u' = 10.62 m/s

when her brother is with her , their speed , vgb = u' * (mg + ms) /( mg + ms + mb)

vgb = 6.81 m/s

at verticl drop of h = 10 m more, let the speed of them be v

using conservation of energy

0.5 * (mg + ms + mb) * v^2 - 0.5 * (mg + ms + mb) * vgb^2 = (mg + ms + mb)*g*h

v^2 - 6.81^2 = 2 * 9.8 * 10

v = 15.57 m/s

their speed at the bottom is 15.57 m/s

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