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The dynamics of a tennis ball are modelled by assuming that its velocity, v(t), is primarily horizontal and the rate of reduction of the velocity is proportional to the square of the velocity (gravity is neglected). (v¹+kt)-¹, where vo = v(0) is the initial speed and k is a (b) A tennis ball is served at an initial speed of 70 m s-¹. After 0.4 s, its speed has reduced to 40 m s-¹. Show that k≈ 0.027 m-¹. (a) Show that v(t) constant. = (c) If the ball is returned with an initial speed of 50 m s-¹ and takes 0.7 s to reach the other player, estimate its speed when it reaches the other player.

The dynamics of a tennis ball are modelled by assuming that its velocity, v(t), is primarily horizontal and the rate of reduction of the velocity is proportional to the square of the velocity (gravity is neglected). (v¹+kt)-¹, where vo = v(0) is the initial speed and k is a (b) A tennis ball is served at an initial speed of 70 m s-¹. After 0.4 s, its speed has reduced to 40 m s-¹. Show that k≈ 0.027 m-¹. (a) Show that v(t) constant. = (c) If the ball is returned with an initial speed of 50 m s-¹ and takes 0.7 s to reach the other player, estimate its speed when it reaches the other player.

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4. The dynamics of a tennis ball are modelled by assuming that its velocity, v(t), is primarily horizontal and the rate of reduction of the velocity is proportional to the square of the velocity (gravity is neglected). (a) Show that v(t) = = constant. (v¹+kt)-¹, where vo = v(0) is the initial speed and k is a (b) A tennis ball is served at an initial speed of 70 m s-¹. After 0.4 s, its speed has reduced to 40 m s-¹. Show that k≈ 0.027 m-1. (c) If the ball is returned with an initial speed of 50 m s-¹ and takes 0.7 s to reach the other player, estimate its speed when it reaches the other player.
Transcribed Image Text:4. The dynamics of a tennis ball are modelled by assuming that its velocity, v(t), is primarily horizontal and the rate of reduction of the velocity is proportional to the square of the velocity (gravity is neglected). (a) Show that v(t) = = constant. (v¹+kt)-¹, where vo = v(0) is the initial speed and k is a (b) A tennis ball is served at an initial speed of 70 m s-¹. After 0.4 s, its speed has reduced to 40 m s-¹. Show that k≈ 0.027 m-1. (c) If the ball is returned with an initial speed of 50 m s-¹ and takes 0.7 s to reach the other player, estimate its speed when it reaches the other player.
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