A santol rolls across a table with a speed of 2m/s and falls off the edge. If it lands 3m from the edge of the table, what height does it fall?
horizontal problem:
no horizontal force so constant horizontal momentum, constant velocity u
3 meters = u t = 2 t
so t = 1.5 seconds
vertical problem:
falls h meters in 1.5 seconds with zero initial v
0 = h + 0 * 1.5 - 4.9 t^2
h = 4.9 * 2.25 = 11 meters
table is 11 meters high ? Do not sit on the edge.
(maybe 0.3 meters from the table :)
To find the height at which the santol falls, we can use the equations of motion.
The first step is to determine the time it takes for the santol to reach the edge of the table. We can use the equation:
distance = speed × time
In this case, the distance is 3m and the speed is 2m/s. By rearranging the equation, we can solve for time:
time = distance / speed
Substituting the values, we get:
time = 3m / 2m/s = 1.5s
So it takes 1.5 seconds for the santol to reach the edge of the table.
Now, we can use another equation of motion to find the height at which the santol falls. The equation is:
height = initial velocity × time + 0.5 × acceleration × time^2
The initial velocity here is 0 m/s since the santol is no longer rolling but falling freely. The acceleration due to gravity is approximately 9.8 m/s^2. Plugging in the values, we get:
height = 0 × 1.5s + 0.5 × 9.8 m/s^2 × (1.5s)^2
= 0 + 0.5 × 9.8 m/s^2 × 2.25s^2
= 0 + 0.5 × 9.8 m/s^2 × 5.0625s^2
= 0 + 49.05 m
= 49.05 m
Therefore, the santol falls from a height of 49.05 meters.