a man stands on the roof of a building and throws a stone upwards at 15 ms-1. after what time will the stone hit the ground 20m below
you want to find when the height h=0, starting from 20m up:
h(t) = 20 + 15t - 4.9t^2
Thanks a lot
To find the time it takes for the stone to hit the ground, we need to use the equation of motion:
s = ut + (1/2)at^2
Where:
s = distance (20m, in this case)
u = initial velocity (15 m/s)
a = acceleration due to gravity (-9.8 m/s²)
Since the stone is thrown upwards, the acceleration due to gravity will be negative. Plugging in the values into the equation, we get:
20 = 15t + (1/2)(-9.8)t^2
Simplifying the equation, we have:
-4.9t^2 + 15t - 20 = 0
To solve for 't', we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values, we have:
t = (-15 ± √(15^2 - 4(-4.9)(-20))) / (2(-4.9))
Calculating further, we get:
t = (-15 ± √(225 - 392)) / (-9.8)
t = (-15 ± √(-167)) / (-9.8)
The discriminant (b^2 - 4ac) under the square root is negative, which means there are no real solutions. Therefore, the stone will not hit the ground.