A long jumper is thrown with an initial speed of 11m/s at an angle of 20^circ to the horizontal (throw angle). Think of this as the motion of a particle. In this case, (a) How far horizontally can the athlete jump? (b ) What is the maximum height he can reach?

Question

A long jumper is thrown with an initial speed of 11m/s at an angle of 20^circ to the horizontal (throw angle). Think of this as the motion of a particle. In this case, (a) How far horizontally can the athlete jump? (b ) What is the maximum height he can reach?

Answer 1

(a) To find the horizontal distance the athlete can jump, we can use the formula for the range of a projectile:Range = (initial velocity^2 / acceleration due to gravity) * sin(2 * angle of projection)Given:Initial velocity = 11 m/sAngle of projection = 20 degreesFirst, we need to convert the angle to radians:Angle in radians = 20 * π / 180 = 0.349 radiansNow, we can calculate the range:Range = (11^2 / 9.8) * sin(2 * 0.349)Range ≈ 23.7 metersTherefore, the athlete can jump approximately 23.7 meters horizontally.(b) To find the maximum height the athlete can reach, we can use the formula for the maximum height of a projectile:Maximum height = (initial velocity^2 * sin^2(angle of projection)) / (2 * acceleration due to gravity)Given:Initial velocity = 11 m/sAngle of projection = 20 degreesFirst, we need to convert the angle to radians:Angle in radians = 20 * π / 180 = 0.349 radiansNow, we can calculate the maximum height:Maximum height = (11^2 * sin^2(0.349)) / (2 * 9.8)Maximum height ≈ 1.2 metersTherefore, the athlete can reach a maximum height of approximately 1.2 meters.

Soru

A long jumper is thrown with an initial speed of 11m/s at an angle of 20^circ to the horizontal (throw angle). Think of this as the motion of a particle. In this case, (a) How far horizontally can the athlete jump? (b ) What is the maximum height he can reach?

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