2. You are standing on the centre point (0,0,0) of a football pitch which you have marked out in a grid with horizontal and vertical lines every metre. A ball travels from one goal to the other at a constant speed of 10ms ¹. At time t=0 it passes you. (i) Where will the ball be at t=2s? (ii) What speed will it be travelling at at t=2s? Suppose the match is being watched by somebody moving in a bus, travelling in the opposite direction to the ball at 10ms¹ and they pass by you at the same moment as the ball. Use the Gallilean transformations to figure out: (i) where the ball is in their frame when the time (in their frame) is t=0s (ii) where the ball is in their frame when the time (in their frame) is t=2s (iii) the speed of the ball in their frame when the time (in their frame) is t=2s Now suppose that the bus is travelling in the same direction as the ball. Use the Gallilean transformations to figure out:

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2. You are standing on the centre point (0,0,0) of a football pitch which you have marked
out in a grid with horizontal and vertical lines every metre. A ball travels from one goal to
the other at a constant speed of 10ms ¹. At time t=0 it passes you.
(i) Where will the ball be at t=2s?
(ii) What speed will it be travelling at at t=2s?
Suppose the match is being watched by somebody moving in a bus, travelling in the
opposite direction to the ball at 10ms¹ and they pass by you at the same moment as the
ball. Use the Gallilean transformations to figure out:
(i) where the ball is in their frame when the time (in their frame) is t=0s
(ii) where the ball is in their frame when the time (in their frame) is t=2s
(iii) the speed of the ball in their frame when the time (in their frame) is t=2s
Now suppose that the bus is travelling in the same direction as the ball. Use the Gallilean
transformations to figure out:
(iv) where the ball is in their frame when the time (in their frame) is t=0s
(v) where the ball is in their frame when the time (in their frame) is t=2s
(vi) the speed of the ball in their frame when the time (in their frame) is t=2s
Transcribed Image Text:2. You are standing on the centre point (0,0,0) of a football pitch which you have marked out in a grid with horizontal and vertical lines every metre. A ball travels from one goal to the other at a constant speed of 10ms ¹. At time t=0 it passes you. (i) Where will the ball be at t=2s? (ii) What speed will it be travelling at at t=2s? Suppose the match is being watched by somebody moving in a bus, travelling in the opposite direction to the ball at 10ms¹ and they pass by you at the same moment as the ball. Use the Gallilean transformations to figure out: (i) where the ball is in their frame when the time (in their frame) is t=0s (ii) where the ball is in their frame when the time (in their frame) is t=2s (iii) the speed of the ball in their frame when the time (in their frame) is t=2s Now suppose that the bus is travelling in the same direction as the ball. Use the Gallilean transformations to figure out: (iv) where the ball is in their frame when the time (in their frame) is t=0s (v) where the ball is in their frame when the time (in their frame) is t=2s (vi) the speed of the ball in their frame when the time (in their frame) is t=2s
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