An arrow is shot at an angle 36 of with the horizontal. It has a velocity of 47 m/s.
How high will the arrow go? The acceleration of gravity is 9.8 m/s
To find how high the arrow will go, we can use the concept of projectile motion.
Projectile motion involves the motion of an object (in this case, the arrow) moving in a curved path under the influence of gravity. We can break down the motion of the arrow into horizontal and vertical components.
First, let's find the initial vertical velocity of the arrow. Given the velocity of the arrow (47 m/s) and the angle with the horizontal (36 degrees), we can find the vertical component of the velocity using trigonometry. The vertical component can be calculated as follows:
Vertical velocity (v_y) = velocity (v) * sin(angle)
v_y = 47 m/s * sin(36 degrees)
Now, we can calculate the maximum height reached by the arrow. At the highest point of the arrow's trajectory, the vertical component of its velocity becomes zero. this happens when it is only under the influence of gravity, and no other forces are acting on it.
Using this principle, we can calculate the time taken for the arrow to reach its maximum height (t_max). The time taken to reach the maximum height is the same as the time taken for the arrow to reach the ground.
t_max = (2 * v_y) / g
where g is the acceleration due to gravity (9.8 m/s^2)
Finally, we can calculate the maximum height (h_max) using the formula:
h_max = (v_y^2) / (2 * g)
Using these equations, we can find the height reached by the arrow. Plugging in the given values:
v_y = 47 m/s * sin(36 degrees)
t_max = (2 * v_y) / g
h_max = (v_y^2) / (2 * g)
After evaluating these equations, you will find the height reached by the arrow.
To find out how high the arrow will go, we can use the equations of projectile motion.
Step 1: Determine the vertical component of the initial velocity.
The vertical component of the initial velocity (Vy) can be found using the formula:
Vy = V * sin(θ)
Given:
V = 47 m/s (magnitude of the velocity)
θ = 36° (angle with the horizontal)
Using the formula:
Vy = 47 * sin(36°)
Vy ≈ 28.6 m/s
Step 2: Calculate the time it takes for the arrow to reach its peak.
The time it takes for the arrow to reach its peak (t) can be found using the formula:
t = Vy / g
Given:
g = 9.8 m/s² (acceleration due to gravity)
Using the formula:
t = 28.6 / 9.8
t ≈ 2.92 s
Step 3: Calculate the maximum height reached by the arrow.
The maximum height reached by the arrow (H) can be found using the formula:
H = (Vy²) / (2 * g)
Using the formula:
H = (28.6²) / (2 * 9.8)
H ≈ 41.5 m
Therefore, the arrow will reach a height of approximately 41.5 meters.