OCR A Level: Mechanics 2 - Projectile Motion [June 2008 Q4]

Classical Mechanics Level 3

A golfer hits a ball from a point $O$ on horizontal ground with a velocity of $35\text{ms}^{-1}$ at an angle of $\theta$ above the horizontal. The horizontal range of the ball is $R$ and the time of flight is $t$ seconds.

$(\text{i})$ Express $t$ in terms of $\theta$ , and hence show that $R=125 \sin 2 \theta$ .

The golfer hits the ball so that it lands $110 \text{m}$ from $O$ .

$(\text{ii})$ Calculate the two possible values of $t$ .

Input the sum of the two values of $t$ , correct to 3 significant figures

There are 5 marks available for part (i) and 5 marks for part (ii).

In total, this question is worth 13.9% of all available marks in the paper.

This is part of the set OCR A Level Problems .

The answer is 9.79.

2 solutions

Michael Fuller
Mar 16, 2016

The mark scheme for this question: Large Version

Sudhir Aripirala
May 19, 2016

We know that, A particle suffers same range when it is projected with angle x or 90-x.

Also. The two values of time are (2usinx)/g and (2ucosx)/g . Now, R=(u)^2(sin2x)/(g)..

By substituting u=35m/s and g=9.8 we get

R=125sin2x..

By substituting R=110.. We get sin2x=22/25 from which we get x=0.537..

Sum of values of time= 2u(sinx+cosx)/(g)

By substituting u=35 and x=0.537.. and g=9.8

we get approximately 9.79..