please help me
1)In the movie The avengers, Captain America sees an alien speeder incoming. The speeder passes directly overhead at 3.65m. If he throws his shield straight up with a speed of 7.40 m/s from a height of 1.55 m above the ground (a) will the shied reach the speeder? (b) if so, what velocity? If not, what initial speed must it have to reach the speeder? (c) Find the change in speed of the shield if it were thrown straight down from the speeder to 1.55 m with an initial speed of 7.40 m/s. (d) Does the change in speed of the downward-moving shield agree with the magnitude of the speed change of the shield moving upward between the same elevations? (e) Explain physically why it does or does not agree.
To solve this problem, we can apply the principles of kinematics and use the equations of motion. Let's break down the given information and solve each part of the problem step by step.
(a) To determine if the shield reaches the speeder, we need to compare the time it takes for the shield to reach the speeder with the time it takes for the speeder to pass overhead.
First, let's calculate the time it takes for the speeder to pass overhead. We know the distance (3.65 m), and we can assume the speeder's velocity is constant. Therefore, we can use the following formula:
time = distance / velocity
If we assume the speeder's velocity is v, then the time it takes for the speeder to pass overhead is:
time = 3.65 m / v (equation 1)
Next, we need to calculate the time it takes for the shield to reach the same height as the speeder. The initial height of the shield is given as 1.55 m, and we can use the following kinematic equation to solve for time:
height = initial height + (initial velocity * time) - (0.5 * acceleration * time^2)
Since the shield is thrown straight up, the acceleration is due to gravity and is equal to -9.8 m/s^2. Plugging in the values, we get:
3.65 m = 1.55 m + (7.40 m/s * time) - (0.5 * 9.8 m/s^2 * time^2) (equation 2)
We now have two equations, equation 1 and equation 2, with two unknowns (time and v). We can solve this system of equations simultaneously to find the answer.
(b) If the shield does reach the speeder, we can determine its velocity. Once we find the time from equation 1, we can substitute it back into equation 2 to solve for the velocity:
7.40 m/s = (1.55 m + 7.40 m/s * time) - (0.5 * 9.8 m/s^2 * time^2) (equation 3)
Using the previously solved value for time, we can now solve equation 3 for the velocity.
(c) To find the change in speed of the shield if it were thrown straight down from the speeder to 1.55 m with an initial speed of 7.40 m/s, we can use the same kinematic equation as before. However, this time the initial velocity will be negative since the shield is thrown downwards:
height = initial height + (initial velocity * time) + (0.5 * acceleration * time^2)
Substituting the values, we can find the time it takes for the shield to reach the height of 1.55 m when thrown downwards. Then, we can calculate the final velocity.
(d) To compare the change in speed of the upward-moving shield and the downward-moving shield, we need to calculate their respective changes in speed. The magnitude of the speed change for the upward-moving shield can be found by subtracting the initial velocity from the final velocity obtained in part (b). For the downward-moving shield, we subtract the initial velocity from the final velocity obtained in part (c).
(e) To explain physically why the change in speed may or may not agree, we need to consider factors such as air resistance (if present), different forces acting on the shield during ascent or descent, and the different initial and final velocities.
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