Question

A ball is thrown vertically upwards. It lands on the top of the cliff after a height of 100 m in 7 s. What is the height of the cliff after 9 s? a. 85 m b. 110 m c. 125 m d. 140 m

Answer 1

Using the equations of motion, the initial velocity (u) was calculated, and the height of the cliff after 9 seconds was found to be approximately 59.626 m. This height does not match any of the given answer choices, suggesting there may be a mistake in the question or the choices provided.

Step-by-step explanation:

The student’s question involves determining the height of a cliff from which a ball, thrown vertically upwards, lands after 9 seconds. To solve this, we use the equations of motion for uniformly accelerated motion, with acceleration due to gravity being -9.8 m/s2. To find out the initial velocity (u) with which the ball was thrown, we can use the time it took to reach the 100 m height, which is given as 7 s.

Assuming the upwards direction is positive, we apply the following equation to find u:

s = ut + 0.5at2

Where:

s = displacement in meters (100 m in this case)

u = initial velocity (in m/s)

a = acceleration (-9.8 m/s2 due to gravity)

t = time (7 s in this case)

Thus, the equation becomes:

100 = 7u - 0.5 * 9.8 * 72
u = (100 + 0.5 * 9.8 * 72) / 7

u = (100 + 240.1) / 7

u = 48.586 m/s (approx.)

Now that we have u, we can calculate the height of the cliff after 9 s:

s' = ut' + 0.5at'2
Where t' = 9s

s' = 48.586 * 9 - 0.5 * 9.8 * 92
s' = 437.274 - 396.9

s' = 40.374 m (approx.)

Since the cliff's height after 7 s is 100 m, and the ball has taken an additional 2 seconds to ascend from that point, the height of the cliff after 9 s can be calculated by subtracting the additional height covered in the last 2 seconds from the height at 7 s:

100 m - 40.374 m = 59.626 m

None of the given answer choices match the calculated value. There seems to be an error in the question or the answer choices provided. The closest answer to the calculated value of 59.626 m is not listed among the choices (a) 85 m, (b) 110 m, (c) 125 m, and (d) 140 m.

Answer 2

It lacks sufficient information to calculate the height of the cliff after 9 seconds, such as the ball's initial velocity or more details about its motion.

Step-by-step explanation:

A ball being thrown vertically upwards and landing on a cliff, and we are asked to determine the height of the cliff after 9 seconds. However, without information about the ball's initial velocity or the specifics of its trajectory, we cannot accurately calculate the height of the cliff after 9 seconds based solely on the time provided. This kind of problem typically involves the equations of kinematic motion in one dimension, specifically the equations related to free fall or projectile motion.

In a real scenario of calculating a projectile's height after a certain time has elapsed, one would use the equation h = h0 + v0t + ½gt2, where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and g is the acceleration due to gravity (approximately -9.81 m/s2 when directed downwards). However, as the problem lacks some of this necessary data, the question cannot be resolved with the provided information.