The acceleration due to gravity on a planet other than the earth has a magnitude of 1.50 m/s2. As in examples 6, 7 and 8, a placekicker kicks a football with an initial speed of 20.3 m/s at an angle of 39.4 ° above horizontal. Assume that the ball is kicked on this other planet instead of on the earth. Find (a) the maximum height H and (b) the range that the ball would attain on the other planet.
and your thinking is.....what?
What will be the effect on time in flight with changing g?
To find the maximum height and range of the ball on the other planet, we can use the kinematic equations for projectile motion. However, since the acceleration due to gravity (g) is different on this planet, we need to account for that in our calculations.
(a) To find the maximum height (H) of the ball, we can use the equation for vertical displacement:
H = (v₀² * sin²θ) / (2 * g)
Where:
- v₀ is the initial speed of the ball (20.3 m/s)
- θ is the angle above horizontal (39.4°)
- g is the acceleration due to gravity on the other planet (1.50 m/s²)
(b) To find the range of the ball, we can use the equation for horizontal displacement:
R = (v₀² * sin(2θ)) / g
Now, let's evaluate these equations to find the answers.
Regarding the effect on time in flight with changing g, the time of flight for a projectile doesn't depend on the acceleration due to gravity. It is determined by the initial speed and the launch angle. So, even though the acceleration due to gravity on a different planet may be different, it won't affect the time of flight of the ball.