Okay so the acceleration g on this planet X is 15 m/s^2
I have solved for all answers but this one.
How long would it take the object to reach a height of 14.1 ? For an object thrown upward there are two times it would be at any hieght. Give the going up answer, a comma, and give the going down answer.
How do we go about this?
Assuming that accelerations is constant,
Given: a=15 ms^-2, s=14.1 m
Applying kinematics equation,
v^2 = u^2 + 2as
Find for u since v is 0,
u= sqrt(2 x -15 x -14.1)
= 20.78
Solve for t,
s= ut + 0.5at^2
14.1= 20.78t + 0.5(15)t^2
//Solve quadratic eqn for t
t= 0.564(Ans), -3.33(not possible)
Solving for t,
14.1=20.78t-.5(15)t^2
subtract using a -15m/s^2 (downward acceleration due to gravity)
To calculate the time it takes for an object to reach a specific height on planet X, we can use the kinematic equation for vertical motion. The equation that relates displacement, initial velocity, time, and acceleration is:
h = ut + (1/2)gt^2
Where:
h = height (in meters)
u = initial velocity (in meters per second)
g = acceleration due to gravity (in meters per second squared)
t = time (in seconds)
In this case, since the object is being thrown upward, the initial velocity (u) will be positive. We can rearrange the equation to solve for time (t) by substituting the given values:
14.1 = 0t + (1/2)(15)(t^2)
Now, we need to solve this equation to find the time it takes for the object to reach a height of 14.1 meters.
To solve quadratic equations like this, we'll follow these steps:
1. Multiply both sides of the equation by 2 to eliminate the fraction:
2 * 14.1 = 15t^2
2. Simplify:
28.2 = 15t^2
3. Divide both sides of the equation by 15:
(28.2 / 15) = t^2
4. Take the square root of both sides to solve for t:
t = √(28.2 / 15)
Now, let's calculate the value of t.
Using a calculator or math software, we find that t ≈ 1.138 seconds.
So, it takes the object approximately 1.138 seconds to reach a height of 14.1 meters while going upward on planet X.
Now, since the object reaches the same height again when it comes back down, we need to double the time to find the total time it takes for the object to be at the height of 14.1 meters. Therefore, the going-up answer is 1.138 seconds, and the going-down answer is 2 times that, giving us 2.276 seconds.