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Jamieson is competing in his school’s 3.0-metre diving competition. For his last dive, he is performing a forward somersault. The duration of the dive must be exactly 1.75 seconds or he will under- or over-rotate before hitting the water. He jumps upwards off the board with a vertical velocity of 6.0 m s−1 and takes $t$t​ seconds to land in the pool. Take the upwards direction as positive.Which of the following correctly describes the displacement of the diver as he hits the water?A0 mB3.0 mC−3.0 mD6.0 m

Question

Jamieson is competing in his school’s 3.0-metre diving competition. For his last dive, he is performing a forward somersault. The duration of the dive must be exactly 1.75 seconds or he will under- or over-rotate before hitting the water. He jumps upwards off the board with a vertical velocity of 6.0 m s−1 and takes ttt​ seconds to land in the pool. Take the upwards direction as positive.Which of the following correctly describes the displacement of the diver as he hits the water?A0 mB3.0 mC−3.0 mD6.0 m

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Solution

To solve this problem, we need to use the equation of motion that relates displacement (s), initial velocity (u), time (t), and acceleration (a). The equation is:

s = ut + 0.5at^2

In this case, the initial velocity (u) is 6.0 m/s, the time (t) is 1.75 seconds, and the acceleration (a) is -9.8 m/s^2 (negative because it's acting downwards due to gravity).

Substituting these values into the equation gives:

s = (6.0 m/s * 1.75 s) + 0.5 * -9.8 m/s^2 * (1.75 s)^2

Solving this gives:

s = 10.5 m - 15 m = -4.5 m

This means the diver is 4.5 m below the point from where he started his dive. However, the diving board is 3.0 m above the water. So, the displacement of the diver as he hits the water is -4.5 m + 3.0 m = -1.5 m.

None of the options A, B, C, or D is correct. The displacement of the diver as he hits the water is -1.5 m.

This problem has been solved

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