Batman is leaping from building to building in pursuit of Joker. The rooftop of

Question

Batman is leaping from building to building in pursuit of Joker. The rooftop of the next building is 10 meters away and 15 meters below the roof he is currently on. If he jumps with a velocity of 5.10 m/s at an angle of 20 degrees above the horizontal, will he make it? (a) what are the components of the initial velocity? (b) How long will he be in the air if he successfully lands on the lower roof? (c) How far will he travel horizontally in the time it takes to land on the lower roof? (d) Compare your answer from (c) to the horizontal distance to the roof of the next building. Does Batman make the jump?

Explanation / Answer

intial velocity = u = 5.10 m/s

(a) initial horizontal velcoity = ux = u cos(theta) = 5.1 * cos(20 deg) = 4.79 m/s

initial vertical velcoity = uy = u sin(theta) = 5.1 * sin(20 deg) = 1.74 m/s

15 = - 1.74 * t + 0.5 * g * t^2

15 = - 1.74 * t + 4.9 * t^2

t = 1.936 s

Horizontal range = ux t = 4.79 * 1.936 = 9.273 m

(b) time in the air if he makes = t = 1.936 s

(c) distance travelled = 9.273 m

(d) horizontal distance travelled is less than distance between 2 buildings

Batman doesn't make the jump

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