Question

Spiderman (87 kg) is patrolling the city, sitting on a rooftop, when his spidey senses goes off. He senses a crime taking place! Spiderman suddenly pushes off the rooftop and experiences a GRF of 5400 N at an angle of 38 degree relative to the right horizontal in a time of 250 ms to leap off teh building. As he leaps he realizes he is out of web! The next building's rooftop is 15 m below the takeoff height and is 35 m away. Does he safely make it to the next rooftop or does he begin to fall to teh ground?

A) what is teh horizontal takeoff velocity?

B) what is the vertical takeoff velocity?

C) how high does spiderman get above his takeoff position?

D) what is the total time in the air?

E) Does he make it to the next rooftop? (show numbers)

Answer 1

A)

component of force

Fx = F*costheta

from newtons law Fx = m*ax = m*(vx - vox)/t

F*costheta = m*(vx-voxx)/t

5400*cos38 = 87*(vx-0)/(250*10^-3)

vx = 12.23 m/s

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B)

along vertical

component of force

Fy = F*sintheta

from newtons law Fy = m*ay = m*(vy - voy)/t

F*sintheta = m*(vy-voy)/t

5400*sin38 = 87*(vy-0)/(250*10^-3)

vy = 9.55 m/s

C)

along vertical after take of

initial velocity vi = vy = 9.55 m/s

acceleration ay = -9.8 m/s^2

final velocity at maimum height vf = 0

displacement y = h

vf^2 - vi^2 = 2*a*y

0 - 9.55^2 = -2*9.8*h

height h = 4.65 m

(D)

along vertical

total displacement y = -15 m

y = vi*t + (1/2)*a*t^2

-15 = 9.55*t - (1/2)*9.8*t^2

time t = 2.98 s

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E)

along horizontal

displacement x = vx*t = 12.23*2.98 = 36.44 > 35

Yes he make it to next roof top