Let's assume the initial velocity of the ball when thrown upwards is v and the height of the cliff is h.
Step 1: Distance-Time Graph
During the upward motion, the distance covered by the ball will increase until it reaches the maximum height and then decrease as it falls back down.
The distance-time graph will be a parabola, with the vertex representing the maximum height attained by the ball.
The equation of motion for the distance covered (d) at any time (t) during the upward motion can be given as:
d = vt - \(\frac 12\)gt2
where g is the acceleration due to gravity (approximately 9.8 m/s2).
During the downward motion, the distance covered will be the total distance from the top of the cliff (h) to the beach (zero level).
Graphically, the distance-time graph will look like a parabola that starts from zero, reaches a peak, and then returns to zero.
Step 2: Velocity-Time Graph
The velocity of the ball will decrease during the upward motion until it reaches the peak, and then increase in the downward motion due to the effect of gravity.
The equation of motion for the velocity (v) at any time (t) during the upward motion can be given as:
v = v - gt
During the downward motion, the velocity will start with the value at the peak and increase at a constant rate (acceleration due to gravity) until it reaches zero at the beach.
Graphically, the velocity-time graph will be a straight line with negative slope during the upward motion and a straight line with positive slope during the downward motion.
Step 3: Displacement-Time Graph
Displacement is the change in position of the ball concerning the reference level (beach).
Displacement is positive during the upward motion and negative during the downward motion.
The equation of motion for the displacement (s) at any time (t) during the upward motion can be given as:
s = vt - \(\frac 12\)gt2
During the downward motion, the displacement will be equal to the height of the cliff (h) minus the distance covered in the downward motion.
Graphically, the displacement-time graph will be a parabola during the upward motion and a straight line with negative slope during the downward motion.
Step 4: Speed-Time Graph
Speed is the magnitude of velocity and is always positive.
During the upward motion, the speed of the ball will decrease until it reaches zero at the peak, and then it will increase during the downward motion.
Graphically, the speed-time graph will start at the initial velocity (v) and decrease until zero at the peak, and then increase with a positive slope during the downward motion.
Now, let's draw the graphs:
(Note: I'm unable to draw graphs directly here, but I'll describe them.)
Distance-Time Graph:
The graph will look like a parabola, starting from zero, reaching a peak, and then returning to zero.
Velocity-Time Graph:
The graph will be a straight line with negative slope during the upward motion and a straight line with positive slope during the downward motion.
Displacement-Time Graph:
The graph will be a parabola during the upward motion and a straight line with negative slope during the downward motion.
Speed-Time Graph:
The graph will start at the initial velocity (v) and decrease until zero at the peak, and then increase with a positive slope during the downward motion.
By analyzing these motion graphs, we can understand the ball's behavior during its journey upwards and downwards from the cliff to the beach. The graphs provide valuable information about the distance covered, velocity, displacement, and speed at different time intervals.
