Question
An arrow is shot straight up into the air at 80.0 m/s.
a) What is the arrow’s maximum height?
b) How long does it take the arrow to reach its maximum height?
a) What is the arrow’s maximum height?
b) How long does it take the arrow to reach its maximum height?
Answers
GPT 3.5
To solve these problems, we will use the equations of motion.
a) We can find the maximum height reached by the arrow using the equation:
v^2 = u^2 + 2as,
where v is the final velocity (0 m/s when the arrow reaches its maximum height), u is the initial velocity (80.0 m/s), a is the acceleration (which is -9.8 m/s^2 due to gravity), and s is the displacement.
Rearranging the equation, we get:
s = (v^2 - u^2) / (2a)
Substituting the given values:
s = (0^2 - (80.0)^2) / (2 * -9.8)
s = -6400 / -19.6
s = 326.53 m
Therefore, the arrow's maximum height is 326.53 m.
b) To find the time it takes for the arrow to reach its maximum height, we can use the equation:
v = u + at
Rearranging the equation, we get:
t = (v - u) / a
Substituting the values:
t = (0 - 80.0) / -9.8
t = 8.16 s
Therefore, it takes the arrow 8.16 seconds to reach its maximum height.
a) We can find the maximum height reached by the arrow using the equation:
v^2 = u^2 + 2as,
where v is the final velocity (0 m/s when the arrow reaches its maximum height), u is the initial velocity (80.0 m/s), a is the acceleration (which is -9.8 m/s^2 due to gravity), and s is the displacement.
Rearranging the equation, we get:
s = (v^2 - u^2) / (2a)
Substituting the given values:
s = (0^2 - (80.0)^2) / (2 * -9.8)
s = -6400 / -19.6
s = 326.53 m
Therefore, the arrow's maximum height is 326.53 m.
b) To find the time it takes for the arrow to reach its maximum height, we can use the equation:
v = u + at
Rearranging the equation, we get:
t = (v - u) / a
Substituting the values:
t = (0 - 80.0) / -9.8
t = 8.16 s
Therefore, it takes the arrow 8.16 seconds to reach its maximum height.