Final answer:
To find the maximum height of the ball on the distant planet, we can analyze the vertical component of its motion. The range of the ball can be determined by analyzing the horizontal component of its motion.
Step-by-step explanation:
To find the maximum height of the ball on the distant planet, we need to analyze the vertical component of its motion. We can use the kinematic equation for vertical motion:
final velocity squared = initial velocity squared + 2 * acceleration * displacement
The ball is launched upwards with an initial velocity of 43 m/s and the only force acting on it is gravity, which is directed downwards and causing a deceleration. The final velocity when the ball reaches its maximum height is 0 m/s, so we can substitute these values into the equation and solve for displacement:
0^2 = 43^2 + 2 * (-g) * displacement
where g is the acceleration due to gravity on the distant planet. Solving for displacement, we get:
displacement = (43^2) / (2 * g)
To find the range of the ball on the distant planet, we can analyze the horizontal component of its motion. The range is the horizontal distance traveled by the ball before it lands. The horizontal velocity of the ball remains constant throughout its flight, so we can use the equation:
range = horizontal velocity * time
The horizontal velocity can be found by multiplying the initial velocity (43 m/s) by the cosine of the launch angle (60 degrees). The time can be found by dividing the total flight time of the ball by 2, as the ball takes the same amount of time to reach the maximum height and to return to the same level as the tee. The total flight time can be found using the equation:
total flight time = 2 * (vertical velocity) / g
where the vertical velocity is the vertical component of the initial velocity, which is equal to the initial velocity multiplied by the sine of the launch angle.