(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A boat is 50.0m from the base of a cliff, fleeing at 5.0m/s. A gun, mounted on the edge of the cliff fires a shell at 40.0m/s and hits the boat when it has fled another 50.0m.

a) At what angel above the horizontal must the gun be aimed so that the shell will hit the target?

b) How high is the cliff?

c) With what velocity does the shell hit the boat?

Boat

v = 5m/s

d = 50m

t = 10s

Shell

v_{i}= 40m/s

a = 9.8m/s^{2}

t = 10s

2. Relevant equations

All the ones dealing with motion

3. The attempt at a solution

a)

v_{ix}= 100/10

v_{ix}= 10m/s

SinΘ = o/h

SinΘ = 10/40

SinΘ = 0.25

Θ = 14^{o}

Therefore the angle about the horizontal must be 14^{o}to hit the boat.

b)

v_{yf}= v_{yi}+aΔt

v_{yf}= 38.7298+(10x9.8)

v_{yf}= 38.7298+98

v_{yf}= 136.73m/s

Δy = ((136.73+38.7298)/2)x10

Δy = 87.7x10

Δy = 877m

Δy = 880m

Therefore the cliff is 880m high.

c)

v_{f}^{2}= 38.72^{2}+(2x9.8x880)

v_{f}^{2}= 1500+17195

v_{f}^{2}= 18695

v_{f}= 136.73m/s

v_{f}= 140m/s

x^{2}= 136.73^{2}+100

x^{2}= 19700

x = 140.357m/s

x = 140m/s

TanΘ = 140/10

TanΘ = 13.673

Θ = 85.818^{o}

Θ = 86^{o}

Therefore the shell hit the boat at 140m/s [86^{o}below the horizontal]

Are these answers correct? I find the questions when two objects move at the same time very hard to do.

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# Homework Help: Two motion issue

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