A toy car in the figure below runs off the edge of a table that is h = 1.150 m high. The car lands d = 0.410 m from the base of the table.
h = 1.150 m.
Dx = 0.410 m.
a. h = 0.5g*t^2 = 1.150
4.9*t^2 = 1.150
t^2 = 0.235
Tf = 0.484 s. = Fall time.
b. Dx = Xo*Tf = 0.410 m.
Xo * 0.484 = 0.410
Xo = 0.846 m/s. = Speed across table.
To calculate the time it takes for the toy car to hit the ground, we can use the equations of motion.
The first equation we can use is the kinematic equation:
s = ut + 0.5 * a * t^2
Where:
- s is the distance traveled (in this case, the height of the table, h)
- u is the initial velocity (which is 0 because the car starts from rest)
- a is the acceleration due to gravity (which is approximately 9.8 m/s^2)
- t is the time it takes to fall from the table to the ground (what we want to find)
In this case, since the car starts from rest, the initial velocity (u) is 0, and the equation simplifies to:
s = 0.5 * a * t^2
Plugging in the values we have:
s = h = 1.150 m
a = 9.8 m/s^2
1.150 = 0.5 * 9.8 * t^2
Now we can solve for t:
1.150 = 4.9 * t^2
Divide both sides by 4.9:
t^2 = 1.150 / 4.9
t^2 = 0.2347
Now, take the square root of both sides to find t:
t ≈ √0.2347
t ≈ 0.484 seconds
So, it takes approximately 0.484 seconds for the toy car to hit the ground after falling off the table.
To calculate the horizontal distance (d) the car lands from the base of the table, we can use the equation of motion for horizontal motion:
d = v * t
Where:
- d is the horizontal distance
- v is the horizontal velocity of the car
- t is the time
Since there is no horizontal acceleration, the horizontal velocity is constant. Therefore, we can assume that the horizontal velocity at the point of launch is the same as when it lands.
To find the horizontal velocity, we need to consider the vertical motion of the car. From the previous calculations, we know that the car takes 0.484 seconds to reach the ground. During this time, it experiences an acceleration due to gravity, which will affect the horizontal motion as well.
We can use this formula to calculate the horizontal velocity:
v = d / t
Plugging in the values:
d = 0.410 m (given)
t = 0.484 seconds (calculated earlier)
v ≈ 0.410 / 0.484
v ≈ 0.847 m/s
Therefore, the horizontal velocity of the toy car is approximately 0.847 m/s at the point of launch.