In deep space (no gravity), the bolt (arrow) of a crossbow accelerates at 187m/s^2 and attains a speed of 114m/s when it leaves the bow. For how long is it accelerated? Answer in units of m/s
What speed will the bolt have attained 2.8 sec after leaving the crossbow? Answer in units of m/s
How far will the bolt have traveled during the 2.8 sec. Answer in the units of m
t=v/a =114/187 = 0.61 s.
deep space = > v=const => after 2.8 s v= 114m/s,
Distance = 114.0∙2.8 =319.2 m
45wre
To solve these questions, we need to use the equations of motion. The most relevant equation is the equation for uniformly accelerated motion:
V = U + at
where V is the final velocity, U is the initial velocity, a is the acceleration, and t is the time.
Let's solve one question at a time.
Question 1: For how long is the bolt accelerated?
We are given that the acceleration of the bolt is 187 m/s^2 and the final velocity is 114 m/s. We need to find the time (t) for which the bolt is accelerated.
Using the equation above, we can rearrange it to solve for t:
t = (V - U) / a
Substituting the given values:
t = (114 m/s - 0 m/s) / 187 m/s^2
t = 0.6102 seconds
So, the bolt is accelerated for approximately 0.6102 seconds.
Question 2: What speed will the bolt have attained 2.8 seconds after leaving the crossbow?
Here, we are given a new time (2.8 seconds) and need to find the new speed (V).
We can use the same equation and rearrange it to solve for V:
V = U + at
Substituting the given values:
V = 0 m/s + 187 m/s^2 * 2.8 s
V = 523.6 m/s
So, the bolt will have attained a speed of 523.6 m/s after 2.8 seconds.
Question 3: How far will the bolt have traveled during the 2.8 seconds?
To find the distance traveled, we can use a different equation:
S = Ut + (1/2)at^2
Where S is the distance traveled.
Substituting the given values:
S = 0 m/s * 2.8 s + (1/2) * 187 m/s^2 * (2.8 s)^2
S = 705.2 meters
So, the bolt will have traveled a distance of 705.2 meters during the 2.8 seconds.