An object is projected upward from the surface of the earth with an initial speed of 2 km/s. The acceleration of gravity is 9.81 m/s^2. Find the maximum height it reaches. Answer in units of km.
To find the maximum height reached by the object, we can use the kinematic equation:
v^2 = u^2 + 2as
where:
v is the final velocity (0 m/s at the highest point),
u is the initial velocity (2000 m/s),
a is the acceleration (-9.81 m/s^2),
s is the displacement (height reached).
Rearranging the equation to solve for s, we have:
s = (v^2 - u^2) / (2a)
Plugging in the given values:
s = (0^2 - (2000 m/s)^2) / (2 * -9.81 m/s^2)
simplifying:
s = (0 - 4000000 m^2/s^2) / (-19.62 m/s^2)
s = 204110.61 m^2/s^2
Converting meters to kilometers by dividing by 1000:
s = 204.11061 km
Therefore, the maximum height reached by the object is approximately 204.11061 km.