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Mechanics questions - Figuring out direction of motion ?

Q: A ball is kicked towards a target with velocity (98i+218j) from point 0 which is 54m from the goal. The height of the goal us 2.3m

I'm asked to find
i) the time taken to reach the goal in 5 seconds
ii) if the ball goes over or under the goal in the right time
iii) speed and direction as it hits the goal if it doesn't go in

I used Pythagoras to find the speed and got an answer of 5.276 but how do I calculate the motion of direction ?

if it helps I can upload my solutions
(edited 9 years ago)
Original post by T-GiuR
Q: A ball is kicked towards a target with velocity (7i+8j) from point 0 which is 9m from the goal. The height of the goal us 2.3m

I'm asked to find
i) the time taken to reach the goal
ii) if the ball goes over or under the goal
iii) speed and direction as it hits the goal

I've calculated i) and ii) to be 9/7 and 2.19m respectively, so for part iii) I calculated the velocity for both vertical components and horizontal which are -4.6 and 7 respectively.

I used Pythagoras to find the speed and got an answer of 5.276 but how do I calculate the motion of direction ?

if it helps I can upload my solutions


Do you write it as an angle below/above the horizontal, perhaps?
you find the angle by saying

tan-1v/h

where v and h are the moduli of the vertical and horizontal components of velocity
Original post by the bear
you find the angle by saying

tan-1v/h

where v and h are the moduli of the vertical and horizontal components of velocity

Will it always be tan for questions like this ?
Original post by T-GiuR
Will it always be tan for questions like this ?


:yep:
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Avatar for Parallex
Parallex
6
Original post by T-GiuR
Will it always be tan for questions like this ?


Yes, because you have the components.

The component forces will always be the opposite and adjacent values of the triangle.
(edited 9 years ago)
Original post by the bear
you find the angle by saying

tan-1v/h

where v and h are the moduli of the vertical and horizontal components of velocity

just to double check the velocity for both vertical components and horizontal are -4.6 and 7 respectively right ?

As when I used tan^-1 = v/h I got a negative answer of -33.31
(edited 9 years ago)
Original post by Parallex
Yes, because you have the components.

The component forces will always be the opposite and adjacent values of the triangle.

just to double check the velocity for both vertical components and horizontal are -4.6 and 7 respectively right ?

As when I used tan^-1 = v/h I got a negative answer of -33.31
(edited 9 years ago)
Original post by T-GiuR
just to double check the velocity for both vertical components and horizontal are -4.6 and 7 respectively right ?

As when I used tan^-1 = v/h I got a negative answer of -33.31


that means that it is below the horizontal direction... as you would expect on the way down.

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