An archer shoots at a target 60m away. If she shoots at a velocity of 55m/s [right] from a height of 1.5 m, does the arrow reach the target before striking the ground?
To determine if the arrow reaches the target before striking the ground, we need to calculate the time it takes for the arrow to reach the target and compare it to the time it takes for the arrow to fall to the ground.
First, let's calculate the time it takes for the arrow to reach the target using the horizontal motion formula: distance = velocity × time.
The horizontal distance traveled by the arrow is 60m, and the velocity is 55m/s. So, we have:
60m = 55m/s × time
Simplifying the equation:
time = 60m / 55m/s = 1.09s
Now, let's calculate the time it takes for the arrow to fall to the ground using the vertical motion formula: distance = (1/2) × acceleration × time². The acceleration due to gravity is approximately 9.8m/s².
The initial height of the arrow is 1.5m, and the final vertical distance is 0m (the ground level). Using these values in the formula, we get:
0m = (1/2) × 9.8m/s² × time² + 1.5m
Rearranging the equation and simplifying:
(1/2) × 9.8m/s² × time² = -1.5m
4.9m/s² × time² = -1.5m
time² = -1.5m / 4.9m/s²
time² = -0.306s²
Since we cannot have a negative time, it means that the equation has no valid solution, so we can conclude that the arrow does not reach the target before striking the ground.