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?

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