Final answer:
The jumper will jump a distance of approximately 2.97 meters.
Step-by-step explanation:
To find the distance the jumper jumps, we can break down the initial velocity into its horizontal and vertical components. The horizontal component can be found by multiplying the initial speed by the cosine of the angle, while the vertical component can be found by multiplying the initial speed by the sine of the angle. Since the jumper starts and ends at the same height, we can ignore the vertical component and focus on the horizontal component. The horizontal distance covered by the jumper can be calculated using the horizontal component of the initial velocity and the total time in the air. The time in the air can be found using the equation t = 2v/g, where v is the initial vertical component of velocity and g is the acceleration due to gravity. Once we have the time, we can multiply it by the horizontal component of the initial velocity to find the horizontal distance covered.
In this case, the horizontal component of the initial velocity is 8.8 m/s * cos(20°) = 8.23 m/s. The acceleration due to gravity is 9.8 m/s². Plugging these values into the equation t = 2v/g, we get t = 2 * (8.8 m/s * sin(20°)) / 9.8 m/s² = 0.36 s. Finally, we can calculate the horizontal distance covered by multiplying the time in the air by the horizontal component of the initial velocity: distance = 0.36 s * 8.23 m/s = 2.97 m.