Final answer:
The long jumper can jump a distance of 5.67 meters.
Step-by-step explanation:
To find the distance the long jumper can jump, we can break down the initial speed into horizontal and vertical components.
The horizontal component can be found by multiplying the initial speed by the cosine of the takeoff angle (17.1°). The vertical component can be found by multiplying the initial speed by the sine of the takeoff angle.
Since the time of flight is the same for both horizontal and vertical components, we can use the vertical component to calculate the time of flight and then use that time to find the horizontal distance traveled.
So, the horizontal component of the initial speed is 10.3 m/s * cos(17.1°) = 9.85 m/s and the vertical component is 10.3 m/s * sin(17.1°) = 2.84 m/s.
Next, we can use the equation d = vt + (1/2)at^2 to find the vertical distance traveled.
Since the initial vertical velocity is 2.84 m/s and the acceleration due to gravity is -9.8 m/s^2 (negative because it acts in the opposite direction of the initial velocity), the equation becomes 0 = 2.84 t - 4.9 t^2.
Solving for t, we find t = 0.577 s. Now, we can plug this value into the equation d = vt to find the horizontal distance traveled. The horizontal distance is 9.85 m/s * 0.577 s = 5.67 m.
Therefore, the long jumper can jump a distance of approximately 5.67 meters.