Find the speed of the batsman and direction he takes (vectors)

AI Thread Summary
The discussion revolves around calculating the direction and time a fieldsman must run to catch a cricket ball hit by a batsman. The ball travels at 6 m/s, while the fieldsman runs at 10 m/s, with specific angles and distances provided. The correct bearing for the fieldsman to run is determined to be 79.7°. The time taken to reach the ball is calculated using the sine rule and involves finding the length of side TS. The final approach emphasizes using vector analysis to solve the problem accurately.
Richie Smash
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Homework Statement


Hello, I havre problem here relevant to an image I will attach.

''A cricket ball hit by a batsman moves with a speed of 6m/s along a straight line path PQRS, as shown in the diagram. When the ball is at R, a fieldsman starts to run in a straight line from T with a speed of 10m/s.
Given that QRT = 25° and RT = 15m, determine by calculation or by drawing:
(a) the direction in which the fieldsman must run in order to retain the ball.
(b)the time he would take to reach the ball at s.

Homework Equations


V=distance/time

The Attempt at a Solution


I have absolutely no idea on this one I'm afraid.
The answer for part (a) in the backof the book is ''Bearing =79.7° ''

For (b), I drew a perpendicular line to QT. I then found angle RTQ which is 65°, then i worked out the angle from the perpendicular I drew by doing 90°-65° = 25°
From here i used the alternate angle rule to find angles RTS and RST which are 25°.

Then I found angle TRS which is 130° then used the sine rule to find side TS which I got to be 27.2 approx, then divided by 10 to find his speed, for which i got 2.72m/s.

Unfortunately that is also the wrong answer.
 

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Richie Smash said:
no idea
Standatd approach: create a variable for the unknown you wish to find and see what equations you can write. Some promising equations may involve other unknowns, such as the distance RS here. So create a variable for that and try to find a second equation involving it.
 
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I have figured it out, side RS was a vector itself of which I can find the angle necessary to give me a bearing of S from T to find the direction, and I can also use that same triangle with it's angle to fins the length of TS and then subsequently divide to find the time taken.
 
Richie Smash said:
I have figured it out, side RS was a vector itself of which I can find the angle necessary to give me a bearing of S from T to find the direction, and I can also use that same triangle with it's angle to fins the length of TS and then subsequently divide to find the time taken.
Well done.
 
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