Ahmed fills a basket with shopping weighing 10 kg. How much work is being done on the shopping basket when he lifts it verticall
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Answer:
D/H =15
Explanation:
- We can find first the peak height H, taking into consideration, that at the maximum height, the ball will reach momentarily to a stop.
- At this point, we can find the value of H, applying the following kinematic equation:
- If vf=0, if we assume that the positive direction is upwards, we can find the value of H as follows:
- We can use the same equation, to find the value of D, as follows:
- In order to find v₁, we can use the same kinematic equation that we used to get H, but now, we know that v₀ = 0.
- When we replace these values in (1), we find that v₁ = -v₀.
- Replacing in (3), we have:
- Solving for D:
- From (2) we know that H can be expressed as follows:
- ⇒ D = 15 * H
Given data:
* The height of the bullet is 22 m.
* The speed of bullet in the horizontal direction is 524 m/s.
Solution:
By the kinematics equation, the time taken by the bullet to reach the ground is,
where u_y is the vertical velocity component, t is the time taken to reach the ground, g is the acceleration due to gravity, and h is the height of the bullet,
Substituting the known values,
Thus, the time taken by the bullet to reach the ground is 2.12 seconds.
By the kinematics equation for the horizontal motion, the horizontal range of the bullet is,
where u_x is the horizontal component of the velocity, a is the acceleration along the horizontal direction, t is the time taken to reach the ground and R is the horizontal range,
Substituting the known values,
Thus, the horizontal range of the bullet is 1110.9 meters.
Hence, the bullet hit the ground at 1110.9 meters.