The height of a projectile fired upward is given by the formula
s = v0t − 16t^2, where s is the height, v0 is the initial velocity, and t is the time. Find the time for a projectile to return to Earth if it has an initial velocity of 232 ft/s.
This is basically the same question as your other one above this, except you want the
value of s to be 0
https://www.jiskha.com/questions/1818436/the-height-of-a-projectile-fired-upward-is-given-by-the-formula-s-v0t-16t-2-where-s
To find the time it takes for the projectile to return to Earth, we need to set the height (s) equal to zero since the projectile will be on the ground when it returns.
The formula for the height of the projectile is given as:
s = v0t - 16t^2
Substituting the initial velocity (v0) as 232 ft/s and setting s to zero, we have:
0 = 232t - 16t^2
Now we can solve this quadratic equation to find the values of t when the height is zero.
Rearranging the equation, we get:
16t^2 - 232t = 0
Factoring out a common factor:
t(16t - 232) = 0
Setting each factor equal to zero and solving for t, we have:
t = 0 (from the zero factor property)
16t - 232 = 0
Now we solve for t:
16t = 232
t = 232/16
t = 14.5
Therefore, the time it takes for the projectile to return to Earth is 14.5 seconds.
To find the time it takes for a projectile to return to Earth, we need to find the value of t when the height, s, becomes zero.
The formula for the height of the projectile is given as s = v0t − 16t^2. We can set this equation equal to zero and solve for t:
0 = v0t − 16t^2
To solve this quadratic equation, we can rewrite it in the form:
16t^2 - v0t = 0
Next, we can factor out a common term of t:
t(16t - v0) = 0
Now, we have two possible solutions for t: t = 0 or 16t - v0 = 0.
Since we are interested in the time it takes for the projectile to return to Earth, we can discard the solution t = 0, as it represents the initial time.
Now, let's solve for t by setting 16t - v0 = 0:
16t = v0
Divide both sides by 16:
t = v0 / 16
Substituting the given value of v0 = 232 ft/s:
t = 232 ft/s / 16
Simplifying:
t = 14.5 s
Therefore, it takes 14.5 seconds for the projectile to return to Earth if it has an initial velocity of 232 ft/s.