a ball is thrown vertically upward from the ground with the velocity of 30m/s,
a)how long will it take to rise to its highest point?
b)how high does the ball rise?
c)how long after projection will the ball have the velocity of 10m/s upward?
tnx
The variation of height (y, in meters) with time (t, in seconds) is given by the equation
y = 30 t - (g/2) t^2
g is the accelertaion of gravty, 9.8 m/s^2.
(a) The highest value of y is obtained when the velccity V is zero.
V(t) = dy/dt = 30 - gt = 0
Solve for t.
(b) Use the value of t that you get in part (a) to solve for y(t) at that time.
(c) Set V(t) = +10 and solve for t.
To solve these problems, we need to use the equations of motion for objects in free-fall, assuming no air resistance. Here are the steps for solving each part:
a) How long will it take to rise to its highest point?
Step 1: Write down the given information:
- Initial velocity (u) = 30 m/s
- Final velocity (v) at the highest point is 0 m/s (since it comes to rest)
- Acceleration (a) due to gravity = -9.8 m/s² (as it acts in the opposite direction)
Step 2: Use the formula to find the time (t) taken to reach the highest point:
v = u + at
0 = 30 + (-9.8)t
Solving for t:
-9.8t = -30
t = 30/9.8 ≈ 3.06 seconds
So, it will take approximately 3.06 seconds for the ball to rise to its highest point.
b) How high does the ball rise?
To find the maximum height (h), we can use the formula:
h = u*t + (1/2) * a * t²
Substituting the values:
h = 30 * 3.06 + (1/2) * (-9.8) * (3.06)²
Calculating:
h ≈ 46.53 meters
Therefore, the ball will rise to approximately 46.53 meters.
c) How long after projection will the ball have the velocity of 10 m/s upward?
Step 1: Write down the given information:
- Initial velocity (u) = 30 m/s
- Final velocity (v) = 10 m/s
- Acceleration (a) due to gravity = -9.8 m/s² (as it acts in the opposite direction)
Step 2: Use the formula to find the time (t) taken to reach this velocity:
v = u + at
10 = 30 + (-9.8)t
Solving for t:
-9.8t = -20
t = 20/9.8 ≈ 2.04 seconds
Therefore, it will take approximately 2.04 seconds after projection for the ball to have a velocity of 10 m/s upward.