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Suppose you look out the window of a skyscraper and see someone throw a tomato downward from above your window. your window is at a height of 450 feet above the ground. the tomato passes your window after 2 seconds and hits the ground 5 seconds after it was thrown. neglect air resistance, and give units in your answers. (a) find the velocity (with the positive direction pointing up) at which the tomato was thrown.

Respuesta :

carlosego
Formula for height 
 r(t) = a/2 t² + v₀ t + r₀
 where 
 a = acceleration = -32 ft/sec² (gravity) 
 v₀ = initial velocity 
 r₀ = initial height 
 r(t) = -16t² + v₀ t + r₀
 Tomato passes window (height = 450 ft) after 2 seconds: 
 r(2) = 450
 -16(4) + v₀ (2) + r₀ = 450 
 r₀ = 450 + 64 - 2v₀ 
 r₀ = 514 - 2v₀ 
 Tomato hits the ground (height = 0 ft) after 5 seconds: 
 r(5) = 0 
 -16(25) + v₀ (5) + r₀ = 0
 r₀ = 16(25) - 5v₀ 
 r₀ = 400 - 5v₀ 
 
 r₀ = 514 - 2v₀ and r₀ = 400 - 5v₀
 514 - 2v₀ = 400 - 5v₀
 5v₀ - 2v₀ = 400 - 514
 3v₀ = −114 
 v₀ = −38 
 Initial velocity = −38 ft/sec (so tomato was thrown down) 
 (initial height = 590 ft) 
onyebuchinnaji

The velocity at which the tomato was thrown is -38 m/s and the direction is downwards.

The given parameters;

  • height of the window, h = 450 ft
  • first time to pass the window, t = 2 seconds
  • time to hit the ground = 5 seconds

The height traveled by the tomato at the given time is calculated as follows;

[tex]h = h_0 + v_0t - \frac{1}{2} gt^2[/tex]

where;

  • g is acceleration due to gravity = 32 ft/s²

when the time is 2 seconds;

[tex]450 = h_0 + 2v_0 \ - \ (0.5 \times 32 \times 2^2)\\\\450 = h_0 + 2v_0 - 64\\\\450 + 64 = h_0 + 2v_0\\\\514 = h_0 + 2v_0\\\\h_0 = 514 - 2v_0 \ \ ---(1)[/tex]

when the time is 5 seconds;

[tex]0 = h_0 + 5v_0 - (0.5 \times 32 \times 5^2)\\\\0 = h_0 + 5v_0 -400\\\\400 = h_0 + 5v_0[/tex]

from equation 1, the initial velocity of the ball is calculated as follows;

[tex]400 = h_0 + 5v_0\\\\ 400 = (514 - 2v_0) + 5v_0\\\\400 = 514 - 2v_0 + 5v_0\\\\400-514 = 3v_0\\\\-114 = 3v_0\\\\\v_0 = \frac{-114}{3} \\\\v_0 = -38 \ m/s[/tex]

Thus, the velocity at which the tomato was thrown is -38 m/s and the direction is downwards.

Learn more here:https://brainly.com/question/25122220

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