a ball is thrown upwards on the moon with an initial speed of 35m/s .calculate a.time taken to reach the maximum height . b. the maximum height reached by the ball . c. its velocity 3 seconds after it has been thrown.
please help me solve this
find g on the moon. Using that value,
since v = 35-gt, max height, achieved when v=0, is when t = 35/g
h(t) = 35 - 1/2 gt^2
find h(3)
To calculate the time taken to reach the maximum height, the maximum height reached by the ball, and its velocity 3 seconds after being thrown, we can apply the principles of projectile motion.
a. Time taken to reach the maximum height:
The time taken to reach the maximum height can be found using the formula for the time of flight of a projectile. In this case, since the ball is thrown upwards on the moon, the acceleration due to gravity is -1.62 m/s² (approximately one-sixth of the Earth's gravity). The initial vertical velocity (upwards) is 35 m/s, and the final vertical velocity (at the maximum height) will be 0 m/s. Plugging these values into the formula, we can find the time taken:
Time taken = (Final velocity - Initial velocity) / Acceleration
= (0 - 35) / (-1.62)
≈ 21.60 seconds
So, the time taken to reach the maximum height is approximately 21.60 seconds.
b. Maximum height reached by the ball:
To find the maximum height, we can use the formula for the maximum height (h) of a projectile, given the initial vertical velocity and the time taken to reach the maximum height:
h = Initial velocity * Time taken + (1/2) * Acceleration * Time taken²
Plugging in the values:
h = 35 * 21.60 + (1/2) * (-1.62) * (21.60)²
≈ 375.55 meters
Therefore, the maximum height reached by the ball is approximately 375.55 meters.
c. Velocity 3 seconds after being thrown:
To find the velocity of the ball 3 seconds after being thrown, we need to consider the downward acceleration due to gravity. The initial velocity in the upward direction is 35 m/s, and the acceleration due to gravity is -1.62 m/s². We can use the formula for the velocity of a projectile at any given time:
Velocity = Initial velocity + Acceleration * Time
Plugging in the values:
Velocity = 35 + (-1.62) * 3
= 35 - 4.86
≈ 30.14 m/s
So, the velocity of the ball 3 seconds after being thrown is approximately 30.14 m/s.