A stuntman sitting on a tree limb wishes to drop vertically onto a horse galloping under the tree. The constant speed of the horse is 10.0 m/s, and the man is initially 2.75 m above the level of the saddle.
Please Show work!! I am completely lost!
find time it takes to fall 2.75m:
2.75 = 4.9t^2
t = .75s
distance covered by horse in .75s:
d = 10*.75 = 7.5m
man needs to drop down when the horse is 7.5m away. But watch out for the horse's head!
S1=V(0)T+a(g)t^2/2; T=0.75
S2=V(h)T; S2=7.5m
To solve this problem, we can use the equations of motion to determine the time it takes for the stuntman to drop onto the horse.
First, let's calculate the time it takes for the stuntman to fall from the tree limb to the level of the saddle:
Using the equation: s = ut + (1/2)at^2, where s is the distance, u is the initial velocity, t is the time, and a is the acceleration.
The initial velocity, u = 0 since the stuntman is initially at rest.
The distance, s = 2.75 m (height from limb to saddle).
The acceleration, a = 9.8 m/s^2 (acceleration due to gravity).
Substituting the values into the equation:
2.75 = 0*t + (1/2)*9.8*t^2
Simplifying the equation:
2.75 = 4.9t^2
Now, solve for t by rearranging the equation:
t^2 = 2.75/4.9
t^2 = 0.561224
t ≈ √(0.561224)
t ≈ 0.749 s (rounded to three decimal places)
So, it takes approximately 0.749 seconds for the stuntman to fall from the tree limb to the level of the saddle.
Next, let's use this time to calculate the horizontal distance covered by the horse during this time:
The horizontal distance covered by the horse is given by the equation: d = v*t, where d is the horizontal distance, v is the constant speed of the horse, and t is the time.
Substituting the values into the equation:
d = 10.0 m/s * 0.749 s
d ≈ 7.49 m (rounded to two decimal places)
Therefore, the horse covers approximately 7.49 meters horizontally during the time it takes for the stuntman to fall from the tree limb to the level of the saddle.
To find out whether the stuntman will successfully land on the horse, we need to determine the time it takes for the man to fall from the tree limb to the horse.
First, we can calculate how far the horse moves during the time it takes for the man to fall:
Distance = Speed × Time
Given that the speed of the horse is 10.0 m/s, we need to find the time it takes for the man to fall.
The equation for the displacement (falling from rest) can be expressed as:
Displacement = (initial velocity × time) + (0.5 × acceleration × time²)
Since the man starts from rest, the initial velocity is 0. The value of acceleration due to gravity is approximately 9.8 m/s².
The displacement of the man is the distance between the tree limb and the horse, which is 2.75 m. We can rearrange the equation to solve for time:
2.75 = 0.5 × 9.8 × time²
Now, let's solve for time:
2.75 = 4.9 × time²
time² = 2.75 / 4.9
time² ≈ 0.561
Taking the square root of both sides:
time ≈ √0.561
time ≈ 0.75 seconds
So, it will take approximately 0.75 seconds for the man to fall from the tree limb to the horse.
Finally, we need to determine the horizontal distance the horse travels during this time. We can use the equation:
Distance = Speed × Time
Distance = 10.0 m/s × 0.75 s
Distance ≈ 7.5 meters
Therefore, if the horse continues to gallop at a constant speed, and the stuntman falls vertically from the tree limb, he will land approximately 7.5 meters away from the tree limb, which should coincide with the position of the horse.