physics problem. help please

2011-09-26 3:16 pm

An athlete executing a long jump leaving ground at a 30 degree angle and travels 7.8m.
(a) what was the takeoff speed?
(b) if this speed were increased by just 5%, how much longer would the jump ne?

please help. thanks a lot

回答 (1)

天同

2011-09-26 8:22 pm

✔ 最佳答案

(a) Let U be the take off speed
In the horizontal direction: 7.8 = [Ucos(30)].t
i.e. t = 7.8/[Ucos(30)]

In the vertical direction, use equation: s = ut + (1/2)at^2
with s = 0 m, u = U.sin(30), a = -g(=-10 m/s2), t = 7.8/[Ucos(30)]
hence, 0 = U.sin(30).{7.8/[Ucos(30)]} + (1/2).(-10).).{7.8/[Ucos(30)]}^2
solve for U gives U = 9.49 m/s

(b) The new speed = 9.49 x 105/100 ms/ = 9.96 m/s
use equation of motion: s = ut + (1/2)at^2 in the vertical direction
with s = 0 m, u = 9.96sin(30) m/s, a = -10 m/s2, t =?
0 = [9.96sin(30)].t + (1/2).(-10).t^2
i.e. t = 0.996 s

Horizontalt distance travelled = 0.996 x 9.96cos(30) m = 8.59 m
Hence, there is a distance of (8.59 - 7.8) m = 0.79 m longer.

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