A ball is thrown vertically upward with a velocity(v) against the gravity. It reaches the maximum height(h) & returns back to the hand of the thrower with a velocity(u). Draw velocity time graph & position time graph for the situation?
To draw the velocity-time graph and position-time graph for the given situation, we first need to understand the motion of the ball.
Motion of the ball:
1. The ball is thrown vertically upward, which means its initial velocity (v) is positive.
2. Due to gravity, the ball slows down as it moves upward until it reaches its maximum height, where its velocity becomes 0 (u).
3. After reaching the maximum height, the ball starts to move downward, accelerating due to gravity. Its velocity becomes negative.
4. Finally, the ball returns back to the thrower's hand, where its velocity is also negative (u).
Now, let's draw the velocity-time graph:
1. Since the starting velocity is positive (v), the graph will start above the time-axis.
2. The velocity decreases until it reaches 0 at the maximum height.
3. When the ball starts moving downward, the velocity becomes negative.
4. As the ball reaches the hand of the thrower, the velocity is also negative (u).
^
|
+v
|\
| \
| \ Maximum height
| \
| \ /
| \/
________|_____\______> Time
|
-u
Next, let's draw the position-time graph:
1. The initial position will be 0, as it is the starting point for the ball's motion.
2. The ball moves upward, hence the graph will be above the time-axis.
3. At the maximum height, the ball reaches its maximum position (h).
4. After that, the ball starts moving downward towards the thrower's hand.
5. Finally, the ball returns to the initial position (0) in the hand of the thrower.
^
|
|\
| \
| \ Maximum height (h)
| \
| \
________|_____\______> Time
|
|
|
|
|
|
Note: Both graphs are not to scale, and the shape of the curves is indicative of the motion.