Question
A paperweight is thrown straight up with an initial upward velocity of 60 meters per second and an initial height of 6 meters. The acceleration (due to gravity) of the object is given by a(t) = - 9.8 meters per second, where t is in seconds. The equation that describes the paperweight's velocity as a function of time t is:
I’m am sort of stuck on this problem, i am thinking of taking the antiderivative of the acceleration for velocity and then plus the 60 (initial upward velocity). Which turns out to be -9.8t+60+C
But I’m not feeling confident about this answer. The initial height wasn’t used as part of my solution and there should be a way to find C. I am not sure how.
Thank you so much ☺️
I’m am sort of stuck on this problem, i am thinking of taking the antiderivative of the acceleration for velocity and then plus the 60 (initial upward velocity). Which turns out to be -9.8t+60+C
But I’m not feeling confident about this answer. The initial height wasn’t used as part of my solution and there should be a way to find C. I am not sure how.
Thank you so much ☺️
Answers
a(t) = -9.81
v(t) = -9.81t + C
since v(0) = 60,
v(t) = -9.81t + 60
h(t) = -4.9t^2 + 60t + C
since h(0) = 6,
h(t) = -4.9t^2 + 60t + 6
v(t) = -9.81t + C
since v(0) = 60,
v(t) = -9.81t + 60
h(t) = -4.9t^2 + 60t + C
since h(0) = 6,
h(t) = -4.9t^2 + 60t + 6
Its 189.673
Because yes, like oobleck said:
a(t) = -9.81
v(t) = -9.81t + C
since v(0) = 60,
v(t) = -9.81t + 60
h(t) = -4.9t^2 + 60t + C
since h(0) = 6,
h(t) = -4.9t^2 + 60t + 6
Velocity is 0 which means -9.8t+60=0 which means t=60/9.8
Because yes, like oobleck said:
a(t) = -9.81
v(t) = -9.81t + C
since v(0) = 60,
v(t) = -9.81t + 60
h(t) = -4.9t^2 + 60t + C
since h(0) = 6,
h(t) = -4.9t^2 + 60t + 6
Velocity is 0 which means -9.8t+60=0 which means t=60/9.8
Stone
Related Questions
A 0.255 kg ball was thrown vertically upward from a bridge 10.3 meters above the ground with an init...
a stone is thrown straight upward and rises to a maximum vertical height of 40.0m. with what velocit...
A ball is thrown off a low cliff to the beach below. It is thrown into the air with an initial upwar...