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a tennis ball is thrown vertically upwards with a speed of v m/s. the height, H metres, reached by the ball is proportional to the square of v. when v = 30m/s, h = 30m work out the value of:

a) H when v = 20m/s

b) v when H = 15 m 

jakeharris02  Jan 3, 2018
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We have this :

 

H  = kv^2         and we need to find the proportionality constant, k.....so we have

 

30  =  k (30)^2

30  =  k (900)     divide both sides by 900

(1/30)  =  k

 

So....at 20m/s, H  =

 

(1/30)*(20)^2  = 400/30  = 40/3  ≈  13.33 m

 

 

When  H  = 15m,  v  =

 

15  =  (1/30) v^2      multiply both sides by 30

 

450  =  v^2         take the positive root of both sides

 

sqrt (450)  =  v  =  3sqrt(50)  ≈  21.2 m/s

 

 

cool cool cool

CPhill  Jan 3, 2018

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