Physics: force and motion

2012-02-12 12:13 am

A man jumps off a building horizontally at the height of 10 m to escape from a fire. The firemen place a rescue cushion on the ground 1 m to catch him. The cushion is 6 m long and 1 m high. Estimate the maximum and minimum speeds at which the man could jump to land on the cushion.

回答 (1)

天同

2012-02-12 12:46 am

✔ 最佳答案

The minimum speed would casue the man just to land on the cushion at the side nearest to the building, i.e. 1 m from the building.

Consider the horizontal motion: 1 = U.t
where U is the horizontal jumping speed of the man
t is the time taken to land on the cushion.
hence, t = 1/U

Consider the vertical motion, use equation: s = ut + (1/2)at^2
with s = -(10-1) m = -9 m, u = 0, a = -g(=-10 m/s2), t = 1/U
hence, -9 = (1/2).(-10).(1/U)^2
solve for U gives U = 0.745 m/s

Use the same steps to calculate the max speed, but use 7 = U.t instead.
Thus, we have,
-9 = (1/2).(-10).(7/U)^2
U = 5.217 m/s

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