A tomato is thrown upward from a bridge 23 m above the ground at 40 m/sec. Take the acceleration of gravity be equal to 9.8 m/s^2
(a) Give formulas for the acceleration, velocity, and height of the tomato at time t.
(b) How high does the tomato go, and when does it reach its highest point?
(c) How long is it in the air?
To answer these questions, we can use the equations of motion for objects in free fall:
(a) Formulas:
1. Acceleration (a): The tomato is thrown upward, so its acceleration is equal to the acceleration due to gravity, which is -9.8 m/s^2.
a = -9.8 m/s^2
2. Velocity (v): We can use the equation v = u + at, where u is the initial velocity, a is the acceleration, and t is the time.
v = u + at
Given u = 40 m/s and a = -9.8 m/s^2, we can plug in the values to get:
v = 40 - 9.8t
3. Height (h): We can use the equation h = ut + (1/2)at^2, where h is the height of the tomato, u is the initial velocity, a is the acceleration, and t is the time.
h = ut + (1/2)at^2
Given u = 40 m/s and a = -9.8 m/s^2, we can plug in the values to get:
h = 40t - 4.9t^2
(b) To find the highest point, we need to find the time when the velocity becomes zero. So, we can set v = 0 and solve for t:
v = 40 - 9.8t
Setting v = 0, we get:
0 = 40 - 9.8t
9.8t = 40
t = 40 / 9.8
To find the height at the highest point, we substitute this value of t into the height formula:
h = 40t - 4.9t^2
h = 40(40 / 9.8) - 4.9(40 / 9.8)^2
(c) The tomato will be in the air until it reaches the ground, so we need to find the time it takes for the height (h) to become zero. We can solve the height equation:
h = 40t - 4.9t^2
Set h = 0, and solve for t to find the time it takes for the tomato to hit the ground.