To find the time taken for the coin to reach the maximum height, we can use the following equation:
v = u + gt
Where: v is the final velocity (0 m/s at the maximum height) u is the initial velocity (3 m/s) g is the acceleration due to gravity (-9.8 m/s^2, assuming downward direction) t is the time taken to reach the maximum height
Let's substitute the given values into the equation and solve for t:
0 = 3 + (-9.8) * t 9.8t = 3 t ≈ 0.306 seconds
Therefore, it takes approximately 0.306 seconds for the coin to reach the maximum height.
To calculate the maximum height, we can use the equation for vertical motion:
h = u * t + (1/2) * g * t^2
Where: h is the maximum height u is the initial velocity (3 m/s) t is the time taken to reach the maximum height (0.306 seconds) g is the acceleration due to gravity (-9.8 m/s^2, assuming downward direction)
Let's substitute the given values into the equation and solve for h:
h = 3 * 0.306 + (1/2) * (-9.8) * (0.306)^2 h ≈ 0.446 meters
Therefore, the coin reaches a maximum height of approximately 0.446 meters.
To find the velocity and direction of the coin after one second, we can use the equation for vertical motion again:
v = u + gt
Where: v is the final velocity after one second u is the initial velocity (3 m/s) g is the acceleration due to gravity (-9.8 m/s^2, assuming downward direction) t is the time (1 second)
Let's substitute the given values into the equation and solve for v:
v = 3 + (-9.8) * 1 v ≈ -6.8 m/s
The negative sign indicates that the velocity is in the opposite direction to the initial velocity, which means the coin is moving downward.
Therefore, after one second, the coin has a velocity of approximately -6.8 m/s (moving downward).