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Can someone answer this physics question?
A 1.5 m tall archer is standing on a cliff that is 65 m high. he fires an arrow with a speed of 55 m/s at an angle 20 degrees below his horizontal at a 10m high castle wall, 100 m horizontally away from the cliffs base. Determine if the arrow will pass above the castle wall. if it does so determine by how much.
2 Answers
- oldschoolLv 72 years agoFavorite Answer
t = 100/(55cos20) = 1.935s
Height h(t) = 1.5 + 65 - 55sin20 *t - 4.9t²
= 66.5 - 55sin20 *1.935 - 4.9*1.935² = 11.76
Yes by 11.76 - 10 = 1.76m <<<<<<
- electron1Lv 72 years ago
The first step is to calculate the vertical and horizontal components of the arrow’s initial velocity.
Vertical = 55 * -sin 20 (-18.8 m/s)
Horizontal = 55 * cos 20 (51.7 m/s)
Since we know the horizontal distance the arrow moves, we can use it and the horizontal velocity to calculate the time the arrow is moving. Use the following equation.
t = d ÷ v = 100 ÷ 55 * cos 20
This is approximately 1.93 seconds. Let’s use the time and the initial vertical velocity to calculate the final height of the arrow, Use the following equation.
d = vi * t + ½ * a * t^2, a = -9.8 m/s^2
d = 55 * -sin 20 * 100 ÷ 55 * cos 20 + ½ * -9.8 * (100 ÷ 55 * cos 20)^2
d = 100 * -tan 20 – 49,000 ÷ (55 * cos 20^2)
This is approximately -54.7 meters. The negative sign means the arrow is approximately 54.7 meters below its initial height.
Final height = 65 – 54.7
This is approximately 10.3 meters above the ground. Since the wall is 10 meters high, the arrow will pass over the wall.
