Tarzan, in one tree, sights Jane in another tree. He grabs the end of a vine with length 20 m that makes an angle of 45 with the vertical, steps off his tree limb, and swings down and then up to Jane's open arms. When he arrives, his vine makes an angle of 30 with the vertical.
Calculate Tarzan's speed just before he reaches Jane. You can ignore air resistance and the mass of the vine.
2007-02-17 05:39:33 · 3 answers · asked by M 1 in Science & Mathematics ➔ Mathematics
v = {2 g 10 [ 3^(1/2) - 2^(1/2)]}^(1/2) m/s.
= 7.8968... m/s.
The answer depends upon the simple kinematical relationship discovered by Galileo:
v^2 = 2 g d, where ' d ' = the DEPTH of the final point below the initial point.
The best reference point is the vine's fulcrum. Because of the original 45 deg. angle, the initial point is 20/2^(1/2) m or
10 [2^(1/2)] m below the fulcrum. Because of the final 30 deg. angle, the final point is 20 [(3)^(1/2)]/2 m or 10 [3^(1/2)] below the fulcrum. So the depth through which the big swinger has swung towards his sweetie is:
d = 10 [ 3^(1/2) - 2^(1/2)] m.
Then v^2 = 2 g 10 [ 3^(1/2) - 2^(1/2)] m^2/s^2, or
v = {2 g 10 [ 3^(1/2) - 2^(1/2)]}^(1/2) m/s.
Using g = 9.81 m/s^2, that gives v = 7.8968... m/s. QED
Live long and prosper.
2007-02-17 09:03:56 · answer #1 · answered by Dr Spock 6 · 0⤊ 0⤋
i know the respond for a yet no longer b A) since's indoors the midst of 0 tiers (on the instant away forward) and ninety tiers ( on the instant away up) so it is going to bypass the farthest. any lots much less and it is going to fall short. any greater desirable and it is going to bypass up and fall infront of your purpose
2016-11-23 15:10:29 · answer #2 · answered by loveall 4 · 0⤊ 0⤋
use T=2pi x radical(L/g)
T= period . in this case you want to divide T by 2.517 because Tarzan does not complete 1 full period.
L=leangth of vine
g= force of gravity
2007-02-17 05:51:41 · answer #3 · answered by fishburn7 2 · 0⤊ 1⤋