Captain Skyhawk launches tshirts at UTM fans using a compressed gas powered cann

Question

Captain Skyhawk launches tshirts at UTM fans using a compressed gas powered cannon. At time t=0 s the Captain launches a tshirt of mass M with speed Vo at an angle ? from the horizontal. Assume the shirt is fired from ground level. Ignore air resistance and derive expression, in terms of the system parameters M, Vo, ? , and the magnitude of the acceleration due to gravity g for the following...

A. When does the tshirt reach its highest point above the ground (t=tpeak)?

B. How high above the ground H, is the shirt at t=tpeak?

C. Captain Skyhawk is pretty confident about this projectile motion business so takes aim for a fan up the bleachers. Captain Skyhawk estimates the UTM fan is at position (x=80m, y=50m) from the cannon and aims the cannon at an angle of 45 degrees. If possible at all, what launch speed does the captain need to set the cannon to hit the fan with the tshirt?

Explanation / Answer

A)

Tpeak = Vo*sin(theta)/g

B)

at tpeak

H = (Vo*sin(theta))^2/(2g)

c)

Here , using equation of trajectory

y = x * tan(theta) - g*x^2/2(Vo*cos(theta))^2

50 = 80*tan(45) - 9.8*80^2/(2*(V*cos45)^2)

Vo = 45.7 m/s

the initial speed of tshirt must be 45.7 m/s

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