Final answer:
The projectile will reach a maximum height of 490 meters and it will take 10 seconds for it to return to the ground.
Step-by-step explanation:
To calculate how high the projectile will go, we can use the equations of projectile motion. The vertical motion can be treated as free fall, where the initial vertical velocity is 98 m/s and the acceleration due to gravity is -9.8 m/s². Using the equation for displacement in vertical motion, we can calculate the maximum height reached by the projectile. The formula is:
h = (v_i²) / (2g)
where h is the maximum height, v_i is the initial vertical velocity, and g is the acceleration due to gravity:
h = (98²) / (2 * 9.8) = 490 m
So, the projectile will reach a maximum height of 490 meters. To find when it will return to the ground, we can use the equation for time in the vertical motion:
t = (v_f - v_i) / g
where t is the time, v_f is the final vertical velocity (which is 0 at the highest point), v_i is the initial vertical velocity, and g is the acceleration due to gravity. Solving for t:
t = (-v_i) / g = (-98) / (-9.8) = 10 seconds
Therefore, it will take 10 seconds for the projectile to return to the ground.