A long jumper leaves the ground at an angle of 17 degrees to the horizontal and at a speed of 9.43 m/s. How far does he jump? What maximum height does he reach? Answer in units of m. The acceleration due to gravity is 9.8 m/s2.

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To solve this, you need to know how much of his velocity is horizontal and how much is vertical.

Construct a right triangle, starting at the origin, with an angle of 17 degrees, and a hypotenuse of 9.43 m/s. Then use sine and cosine to find the x- and y-values for velocity.

Sin 17 = y/9.43 m/s and y = 2.76 m/s vertical

cos 17 = x/9.43 m/s and x = 9.02 m/s

 

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