Recollect the past 5!

A Particle is projected from a point on the level ground and its height is h when at horizontal distances a and 2a from its point of projection.

Find Velocity of projection

Details And Assumptions

g = 10 SI Unit

a= 10 m

h = 10 m

Report answer upto 2 decimal places.

For the problem writing party


The answer is 18.03.

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2 solutions

Let the initial velocity be x and the angle be θ . Then, the y and x coordinate are given by: y = v sin ( θ ) t 5 t 2 x = v cos ( θ ) t Combining the two, we have y = tan ( θ ) x 5 v 2 cos 2 ( θ ) x 2 Referring to the values given in the question, we have 10 = 10 tan θ 500 v 2 cos 2 θ = 20 tan θ 2000 v 2 cos 2 θ Utilising the last equation, we derive the following: v = 150 cos 2 θ tan θ 10 = 20 3 tan θ From here, it follows that v = 18.03 \text{Let the initial velocity be }x \text{ and the angle be }\theta.\\\text{Then, the }y\mbox{ and }x \text{ coordinate are given by: }\\y=v\sin(\theta)t-5t^2\\x=v\cos(\theta)t\\\text{Combining the two, we have}\\y=\tan(\theta)x-\frac{5}{v^2\cos^2(\theta)}x^2\\\text{}\\\text{Referring to the values given in the question, we have}\\10=10\tan\theta-\frac{500}{v^2\cos^2\theta}=20\tan\theta-\frac{2000}{v^2\cos^2\theta}\\\text{Utilising the last equation, we derive the following:}\\v=\sqrt{\frac{150}{\cos^2\theta\tan\theta}}\\10=\frac{20}{3}\tan\theta\\\text{From here, it follows that }v=18.03

Pranav Singla
May 17, 2018

From simple analysis of the situation we say range to be 3a i.e. 30m = u^2 sin(2theta)/g And from y=x tan(theta)[(1)-(x/R)] we get tan of theta to be 3/2. This by putting in equation one gives answer to be 18.02 m/s

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