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

[Richie Smash]

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.

 

[haruspex]

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.

 

[Richie Smash]

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.

 

[haruspex]

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.