A stone is thrown vertically up word by up word by a boy . It returns to his hands in 3sec . How high does the stone rise ?
top at 3/2 = 1.5 s = t
v = Vi - g t
0 = Vi - g t
so
g t = Vi = 9.81 * 1.5 = 14.7
h = Vi t -4.9 t^2
= 14.7 *1.5 - 4.9(2.25)
= 22 - 11 = 11 meters
note, same as average speed = 14.7/2 times 1.5 seconds
To find the height to which the stone rises, we can use the formula for vertical motion:
h = v0*t + (1/2) * g * t^2
Where:
h = height achieved by the stone
v0 = initial velocity of the stone
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken for the stone to reach its maximum height and return to the boy's hand (3 seconds in this case)
Since the stone was thrown vertically upwards, the initial velocity (v0) would be positive. At its highest point, the stone will momentarily stop moving before descending back into the boy's hand.
To find the initial velocity (v0), we need more information. If the stone was thrown from the ground with an initial velocity of "u" m/s, then when it reaches its highest point, its final velocity will be zero.
Using the equation:
v = u + g*t
0 = u - g*t
Solving for u, we get:
u = g*t
Now, substituting the value of u in the formula for height (h), we have:
h = (g*t)*t + (1/2)*g*t^2
Let's plug in the values to find the height:
h = (9.8 m/s^2) * (3 sec) + (1/2) * (9.8 m/s^2) * (3 sec)^2
h = 29.4 m + 44.1 m
h = 73.5 m
Therefore, the stone rises to a height of 73.5 meters.