5. An archer stands 30 m away from a target that is 122 cm in diameter, as shown below. Theyrelease the arrow at a speed of 60 m/s. Will the arrow hit the target? (Answer=
Question
- An archer stands 30 m away from a target that is 122 cm in diameter, as shown below. Theyrelease the arrow at a speed of 60 m/s. Will the arrow hit the target? (Answer=
Solution
To answer this question, we need to calculate the time it takes for the arrow to reach the target and the vertical distance it would travel in that time due to gravity.
Step 1: Calculate the time it takes for the arrow to reach the target.
The archer is 30 m away from the target and the arrow is shot at a speed of 60 m/s. So, the time it takes for the arrow to reach the target is distance/speed = 30m / 60m/s = 0.5 seconds.
Step 2: Calculate the vertical distance the arrow would travel in that time due to gravity.
The formula to calculate this is 0.5 * g * t^2, where g is the acceleration due to gravity (approximately 9.8 m/s^2) and t is the time. So, the vertical distance is 0.5 * 9.8 m/s^2 * (0.5s)^2 = 0.6125 m or 61.25 cm.
Step 3: Compare the vertical distance the arrow would travel to the diameter of the target.
The target is 122 cm in diameter, so the arrow would hit the target because 61.25 cm is less than 122 cm.
So, yes, the arrow will hit the target.
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