Kinematics 2D Spiderman is standing on the ground 1700 meters away from the base

Question

Kinematics 2D

Spiderman is standing on the ground 1700 meters away from the base of a 325 meters tall building. When he notices that a villain has pushed Mary Jane over the edge. Spiderman takes off in a straight line, and defying gravity, he catches Mary Jane 7s after she started to fall.

(a) Assuming she started from rest, how far has Mary Jane fallen?

(b) Find the displacement of Spiderman and write it in vector notation.

(c) Find the dot product where d1 is Mary Jane's displacement and d2 is Spiderman's displacement. Find the angle between Mary Jane and Spiderman.

Explanation / Answer

(A) Mary have 7 s to fall.

Applying y = ut + at^2 /2

y = 0 + (-9.8)(7^2) /2 = - 240.1 m

Jane has fallen 240.1 m.

(B) to catch Mary Jane, Spiderman have to be at the Mary's position after 7s.

positon = (0 , (325 - 240.1)) = ( 0, 84.9)

initial posiiton = (1700, 0)

displacement vector, r = final posiiton - initial position

= -1700i + 84.9j OR < -1700, -84.9 >

(C) d1 = - 240.1 j

d2 = - 1700i + 84.9 j

d1 . d2 = (- 240.1 j ) . (- 1700i + 84.9 j ) = - 20384.49 ......Ans

d1 . d2 = |d1| |d2| cos@

- 20384.49 = (240.1) (sqrt(1700^2 + 84.9^2)) cos@

cos@ = - 0.05

@ = 92.86 deg

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