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I want to check whether my solution is right or not... beside I have made some correction to the problem so that it will be consistent ( I want to check also this correction).
A body is thrown vertically upwards from a stand of height 30 meters above the ground. If the height h(t) above the ground after t seconds is given by : h(t) =20t-5t^2 +25 meters . Find:
(a) The initial velocity and acceleration and also the velocity and acceleration after t seconds.
(b) The highest point reached by the body.
(c) When the body strikes the ground and its velocity then.
(d) Suppose that instead of being thrown from a stand the body was thrown vertically from the ground with the same acceleration and initial velocity . When will the body strike the ground and find its velocity then.
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This problem is incorrectly formulated:- (I am not sure about that)
I have copied this problem as it is,, and I think that there is a mistake in the problem formulation
Since the stand's height is 30 meters above the ground, the equation should be formulated like this
h(t) =20t-5t^2 +30 meters.
OR instead (that what I will do) correct the height of the stand from 30 to 25 so that the corrected version will be:
A body is thrown vertically upwards from a stand of height 25 meters above the ground. If the height h(t) above the ground after t seconds is given by : h(t) =20t-5t^2 +25 meters.
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(a) The initial velocity and acceleration and also the velocity and acceleration after t seconds.
the velocity:
v(t) = (dh/dt) = 20-10t m/s
initial velocity is when t=0
v(0) = 20 m/s
the acceleration:
a(t) = (dv/dt) = -10 m/s^2
so a=-10 m/s^2
....................................
(b) The highest point reached by the body.
the highest point is when v(t) = 20-20t = 0
20-10t=0
t = 2 seconds
the highest point can be given using h(t) =20t-5t^2 +25
h(2) =20(2)-5(2)^2 +25 = 45 m
......................................
(c) When the body strikes the ground and its velocity then.
the body strikes the ground when h(t) =20t-5t^2 +25 = 0
20t-5t^2 +25 = 0
using the quadratic formula
t = -1 seconds and t = 5 seconds
**************************
I want to know what each result represents, and what is the meaning of the minus sign in (t=-1)
**************************
the velocity can be given
v(t) = 20-10t m/s
v(-1) = 30 m/s
v(5) = -30 m/s
**********************
I want to know what each result represents, and what is the meaning of the minus sign in v(5) = -30 m/s
**********************
.............................
(d) Suppose that instead of being thrown from a stand the body was thrown vertically from the ground with the same acceleration and initial velocity . When will the body strike the ground and find its velocity then.
Here I changes the equation of height to be
h(t) =20t-5t^2
the equation of velocity (not changed)
v(t) = 20-10t m/s
the body will strike the ground when h(t) =20t-5t^2 = 0
t(20-5t) = 0
t=0 seconds and t = 4 seconds
**************************
I want to know what each result represents.
**************************
the velocity can be given v(t) = 20-10t m/s
v(0) = 20 m/s
v(4) = -20 m/s
**************************
I want to know what each result represents. and what is the meaning of the minus sign in v(4) = -20 m/s
**************************
Homework Statement
A body is thrown vertically upwards from a stand of height 30 meters above the ground. If the height h(t) above the ground after t seconds is given by : h(t) =20t-5t^2 +25 meters . Find:
(a) The initial velocity and acceleration and also the velocity and acceleration after t seconds.
(b) The highest point reached by the body.
(c) When the body strikes the ground and its velocity then.
(d) Suppose that instead of being thrown from a stand the body was thrown vertically from the ground with the same acceleration and initial velocity . When will the body strike the ground and find its velocity then.
******************************
This problem is incorrectly formulated:- (I am not sure about that)
I have copied this problem as it is,, and I think that there is a mistake in the problem formulation
Since the stand's height is 30 meters above the ground, the equation should be formulated like this
h(t) =20t-5t^2 +30 meters.
OR instead (that what I will do) correct the height of the stand from 30 to 25 so that the corrected version will be:
A body is thrown vertically upwards from a stand of height 25 meters above the ground. If the height h(t) above the ground after t seconds is given by : h(t) =20t-5t^2 +25 meters.
******************************
Homework Equations
The Attempt at a Solution
(a) The initial velocity and acceleration and also the velocity and acceleration after t seconds.
the velocity:
v(t) = (dh/dt) = 20-10t m/s
initial velocity is when t=0
v(0) = 20 m/s
the acceleration:
a(t) = (dv/dt) = -10 m/s^2
so a=-10 m/s^2
....................................
(b) The highest point reached by the body.
the highest point is when v(t) = 20-20t = 0
20-10t=0
t = 2 seconds
the highest point can be given using h(t) =20t-5t^2 +25
h(2) =20(2)-5(2)^2 +25 = 45 m
......................................
(c) When the body strikes the ground and its velocity then.
the body strikes the ground when h(t) =20t-5t^2 +25 = 0
20t-5t^2 +25 = 0
using the quadratic formula
t = -1 seconds and t = 5 seconds
**************************
I want to know what each result represents, and what is the meaning of the minus sign in (t=-1)
**************************
the velocity can be given
v(t) = 20-10t m/s
v(-1) = 30 m/s
v(5) = -30 m/s
**********************
I want to know what each result represents, and what is the meaning of the minus sign in v(5) = -30 m/s
**********************
.............................
(d) Suppose that instead of being thrown from a stand the body was thrown vertically from the ground with the same acceleration and initial velocity . When will the body strike the ground and find its velocity then.
Here I changes the equation of height to be
h(t) =20t-5t^2
the equation of velocity (not changed)
v(t) = 20-10t m/s
the body will strike the ground when h(t) =20t-5t^2 = 0
t(20-5t) = 0
t=0 seconds and t = 4 seconds
**************************
I want to know what each result represents.
**************************
the velocity can be given v(t) = 20-10t m/s
v(0) = 20 m/s
v(4) = -20 m/s
**************************
I want to know what each result represents. and what is the meaning of the minus sign in v(4) = -20 m/s
**************************
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