Question

Standing on a balcony, you throw your keys to a friend standing on the ground below. 1.1 seconds after you release the keys, they have an instantaneous velocity of 15.4 m/s, directed 52deg below the horizontal. What initial velocity did you give them?

Magnitude?

Direction?

Answer 1

Solution)

velocity after 1.1 sec

V= 15.4 m/s

We have; in horizontal direction Vx = 15.4 cos(52) = 9.48 m/s

in vertical direction Vy= 15.4 sin(52) = 12.13 m/s

Initial horizontal velcoity Ux = Vx = 9.48 m/s (since no acceleration in horizontal direction)

Initial vertical velocity Uy = Vy-gt = 12.13 - 9.8*1.1= 1.35 m/s

Magnitude of net velocity = sqrt(9.48^2+1.35^2) = 9.57 m/s (Ans)

Direction arctan(1.35/9.48) = 8.1 degrees below horizontal

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