A hunter shoots an arrow at a deer running directly away from him. When the arrow leaves the bow, the deer is at distance of 42 m. When the arrow strikes, the deer is at a distance of 51 m. The speed of the arrow is 68 m/s.
What must have been the speed of the deer? (m/s) How long did the arrow take to travel to the deer? (s)
how long does it take the arrow to travel the 51m?
time = distance/speed = 51m / (68m/s) = 0.75s
so, since speed = distance/time, the deer's speed was (51-42)m/0.75s = 12 m/s
Well, the speed of the arrow is 68 m/s, but unfortunately, I don't have any information about the speed of the deer. But I bet the deer was pretty fast, trying to avoid getting hit by an arrow! As for how long the arrow took to travel to the deer, I think that would depend on how well the hunter aimed. Maybe he took a little too long to aim, and the deer managed to cover some distance. It's a real nail-biter!
To find the speed of the deer, we need to find the relative speed of the deer with respect to the arrow.
Step 1: Calculate the change in distance between the deer and the hunter.
Change in distance = Final distance - Initial distance
Change in distance = 51 m - 42 m
Change in distance = 9 m
Step 2: Calculate the time taken by the arrow to cover the change in distance.
Speed = Distance / Time
68 m/s = 9 m / Time
Step 3: Rearrange the equation to solve for time.
Time = Distance / Speed
Time = 9 m / 68 m/s
Time ≈ 0.1324 s
Therefore, the arrow took approximately 0.1324 seconds to reach the deer.
Step 4: Calculate the speed of the deer.
Relative Speed = Distance / Time
Relative Speed = 9 m / 0.1324 s
Relative Speed ≈ 67.99 m/s
Since the speed of the arrow is 68 m/s, the speed of the deer must also be approximately 67.99 m/s.
To find the speed of the deer, we can use the concept of relative velocity. Relative velocity is the difference between two velocities.
Let's denote the speed of the deer as v_deer. Since the deer is running directly away from the hunter, its velocity is negative (-v_deer). The velocity of the arrow is given as 68 m/s.
When the arrow hits the deer, the relative velocity between them is zero. This is because the arrow catches up to the deer.
Using the formula for relative velocity, we can set up the equation:
velocity of the deer - velocity of the arrow = 0
-v_deer - 68 m/s = 0
Solving this equation, we find:
-v_deer = 68 m/s
v_deer = -68 m/s
However, the velocity of an object cannot be negative in this context since it represents speed (magnitude) only. So we take the magnitude of the velocity:
v_deer = |-68 m/s| = 68 m/s
Therefore, the speed of the deer must have been 68 m/s.
To find the time it took for the arrow to travel to the deer, we can use the equation:
distance = speed × time
The initial distance between the hunter and the deer is given as 42 m, and the final distance (when the arrow strikes) is given as 51 m. The speed of the arrow is given as 68 m/s.
Let's denote the time taken by the arrow as t.
Using the formula above, we can set up the equation:
51 m - 42 m = 68 m/s × t
Solving this equation, we find:
9 m = 68 m/s × t
t = 9 m / (68 m/s)
t ≈ 0.132 s
Therefore, the arrow took approximately 0.132 seconds to travel to the deer.