Physics, 02.08.2019 07:30 AmityHeart

Bob has just finished climbing a sheer cliff above a beach, and wants to figure out how high he climbed. all he has to use, however, is a baseball, a stopwatch, and friend on the ground below with a long measuring tape. bob is a pitcher, and knows that the fastest he can throw the ball is about 32.5m/s. bob starts the stopwatch as he throws the ball and watches carefully. the ball rises and then falls, and after 0.510 seconds the ball is once again level with bob. bob's friend then measures that the ball landed 123m from the base of the cliff. how high is bob, if the ball started from 2m?

Answers: 1

Show answers

Answers

In order to solve this problem, you need to divide the motion of the ball into its vertical and horizontal components.

Consider the vertical component: the time taken to rise and fall at Bob's level again is twice the time taken to reach the highest point. At the highest point, the speed (v₁) is zero. Therefore, we can calculate the vertical component of the initial velocity considering it is a decelerated motion:
v₁ = vy - g·t
vy = g·t
= (9.8)·(0.255)
= 2.5 m/s

Since you know the magnitude of the initial speed and now also the vertical component, you can calculate the angle of the direction:
vy = v₀ · sinα
α = sin⁻¹ (vy / v₀)
   = sin⁻¹ (0.0769)
   = 4.4°

Now, we can calculate the horizontal component of the initial velocity:
vx = v₀ · cosα
= 32.5 · cos(4.4)
= 32.4 m/s

Horizontally, the ball is moving at a constant speed, therefore we can find the total time traveled:
d = vx · t
t = d / vx
= 123 / 32.4
= 3.796 s

This is the time taken for the ball to reach the ground from when Bob launches it. Subtracting the time taken to rise and fall again at Bob's level, you get the time taken to reach the ground from Bob's level:
t₂ = t - t₁
= 3.796 - 0.510
= 3.286 s

This last part of the motion is a free fall from a position h₀ = 2 meters above the cliff (which is Bob's height), with initial speed vy = 2.5 m/s during a time t₂ = 3.286 s; you can then solve for the height of the cliff:
h = h₀ + vy · t₂ + (1/2) · g · t₂²
   = -2 + (2.5)(3.286) + (0.5)(9.8)(3.286)²
   = -2 + 8.215 + 52.909
   = 60.124 m

Therefore, the correct answer is: the cliff is 60m high.

Answer from: layla07

The speed is defined as the distance per unit of time. The unit of speed is m/s. The speed is a scalar quantity which means it only depends on the magnitude.

In order to solve this problem, you need to divide the motion of the ball into its vertical and horizontal components.

At the highest point, the speed (v₁) is zero. Therefore, we can calculate the vertical component of the initial velocity considering it is a decelerated motion

: $v_1 = vy - g*t\\\\ = (9.8)*(0.255)\\ = 2.5 m/s$

Now, we can calculate the angle of the direction: $vy = v_0 *sina\\a = sin^-1 (\frac{vy}{ v₀}) \\ = sin^-1 (0.0769) = 4.4* 10^-^{10}$ m/s

Now, we can calculate the horizontal component of the initial velocity:

$vx = v_0* cosa\\ = 32.5*cos(4.4) \\= 32.4 m/s$

Horizontally, the ball is moving at a constant speed, therefore we can find the total time traveled:

$d = vx * t\\\\t = \frac{d}{vx} \\ \\= \frac{123}{32.4}\\ \\ = 3.796 s$

The time taken by the bob is:-

$t₂ = t_2 - t_1\\ = 3.796 - 0.510\\ = 3.286 s$

To find the height, the formula we are using it:-

$h = h_0 + vy * t₂ + \frac{1}{2} * g * t_2^2\\ = -2 + (2.5)(3.286) + (0.5)(9.8)(3.286)^2\\ = -2 + 8.215 + 52.909 \\ = 60.124 m$

Therefore, the correct solution is: the cliff is 60m high.

For more information, refer to the link:-

link

Answer from: Quest

The duration of a photographic flash is related to an rc time constantly

Answer from: Quest

if the person is shown to have +90n, then ans is -10n.

if the person is shown to have -90n, then ans is +10n.

Another question on Physics

Physics, 21.06.2019 21:30

Ascientist is tracking an object orbiting the sun that is found between mars and jupiter. in order to classify the object as an asteroid, it must be at least

Answers: 1

Answer

Physics, 22.06.2019 03:30

Acoyote chasing a rabbit is moving 8.00 m/s due east at one moment and 8.80 m/s due south 4.25 s later. let the x axis point due east and the y axis point due north. find the direction of the coyote's average acceleration during that time.

Answers: 1

Answer

Physics, 22.06.2019 16:00

Marvin records scientific data about lake superior. for which property has marvin forgotten to use an si unit of measurement? shore length high temperature low temperature annual precipitation

Answers: 3

Answer

Physics, 22.06.2019 16:30

Atank has a shape of a cone with a radius at the top of 2 m and a height of 5 m. the tank also has a 1 m spout at the top of the tank. the tank is filled with water up to a height of 2 m. find the work needed to pump all the water out the top of the spout. (use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3.)

Answers: 1

Answer

You know the right answer?

Bob has just finished climbing a sheer cliff above a beach, and wants to figure out how high he clim...

Questions