A toy car in the figure below runs off the edge of a table that is h = 1.375 m high. The car lands d = 0.375 m from the base of the table.How fast was the car going on the table?
To find the speed of the car on the table before it runs off, we can use the principle of conservation of energy. The car will lose potential energy equal to its gain in kinetic energy.
Step 1: Identify the known variables:
- Initial height of the car on the table: h = 1.375 m
- Distance the car traveled horizontally: d = 0.375 m
Step 2: Calculate the potential energy:
The potential energy of an object at height h is given by the formula PE = m * g * h, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Step 3: Calculate the kinetic energy:
The kinetic energy of an object is given by the formula KE = (1/2) * m * v^2, where v is the velocity or speed of the object.
Step 4: Equate potential energy to kinetic energy:
Since the car loses its potential energy but gains kinetic energy, we can equate the two expressions:
PE = KE
m * g * h = (1/2) * m * v^2
Step 5: Solve for the speed:
Rearrange the equation to solve for v:
v = sqrt((2 * g * h) / 1)
Substituting the known values:
v = sqrt((2 * 9.8 * 1.375) / 1)
v ≈ 5.22 m/s
So, the car was going approximately 5.22 m/s on the table before running off.
Let Vo be the initial speed.
Vo remains the horizontal velocity component while it falls.
Vo *(fall time) = 0.375 m
Compute the time T that it takes to fall H = 1.375 m, and use that in the equation above to solve for Vo.
(1/2)gT^2 = H
T = sqrt(2H/g)