Respuesta :
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.
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.
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
: [tex]v_1 = vy - g*t\\\\ = (9.8)*(0.255)\\ = 2.5 m/s[/tex]
Now, we can calculate the angle of the direction: [tex]vy = v_0 *sina\\a = sin^-1 (\frac{vy}{ v₀}) \\ = sin^-1 (0.0769) = 4.4* 10^-^{10}[/tex]m/s
Now, we can calculate the horizontal component of the initial velocity:
[tex]vx = v_0* cosa\\ = 32.5*cos(4.4) \\= 32.4 m/s[/tex]
Horizontally, the ball is moving at a constant speed, therefore we can find the total time traveled:
[tex]d = vx * t\\\\t = \frac{d}{vx} \\ \\= \frac{123}{32.4}\\ \\ = 3.796 s[/tex]
The time taken by the bob is:-
[tex]t₂ = t_2 - t_1\\ = 3.796 - 0.510\\ = 3.286 s[/tex]
To find the height, the formula we are using it:-
[tex]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[/tex]
Therefore, the correct solution is: the cliff is 60m high.
For more information, refer to the link:-
https://brainly.com/question/22610586
