If an object is thrown vertically upward with an initial velocity of v, from an original position of s, the height h at any time t is given by: h=-16t^2+vt+s(where h and s are in ft, t is in seconds and v is in ft/sec)
A package is thrown downward with an initial velocity of -5 ft/sec from a helicopter at 300 ft. A) what is the height of the package in 2 sec? B) how long does it take to hit the ground?
Round answer to 2 decimals Enter: blank ft,blank sec.
A. h = ho - (Vo*t + 16t^2).
h = 300 - (5*2 + 16*2^2 )= 226 Ft above
gnd.
B. h = 300 - (5t + 16t^2 = 0.
300 - 5t -16t^2 = 0.
-16t^2 - 5t + 300 = 0.
Use Quad. Formula>
t = 4.18 s.
To find the height of the package in 2 seconds, we can use the equation h = -16t^2 + vt + s, where h represents the height, t represents time, v represents the initial velocity, and s represents the initial position.
Given: v = -5 ft/sec and s = 300 ft. We need to calculate h when t = 2 seconds.
A) Height of the package in 2 seconds:
Substitute the given values into the equation:
h = -16(2)^2 + (-5)(2) + 300
h = -16(4) -10 + 300
h = -64 - 10 + 300
h = 226 ft
Therefore, the height of the package after 2 seconds is 226 ft.
B) To determine how long it takes for the package to hit the ground, we need to find the time when h = 0 (ground level).
Using the same equation, we set h = 0 and solve for t:
0 = -16t^2 - 5t + 300
Rearranging the equation:
16t^2 + 5t - 300 = 0
To solve this quadratic equation, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac))/(2a)
From the quadratic equation, a = 16, b = 5, and c = -300. Substituting these values into the quadratic formula:
t = (-(5) ± √((5)^2 - 4(16)(-300))) / (2(16))
t = (-5 ± √(25 + 19200)) / (32)
t = (-5 ± √19225) / 32
Calculating the square root:
t = (-5 ± 139) / 32
Therefore, the two possible solutions for t are:
t = (-5 + 139) / 32 ≈ 4.17 seconds
t = (-5 - 139) / 32 ≈ -4.72 seconds
Since time cannot be negative in this case, we discard the negative value.
Hence, it takes approximately 4.17 seconds for the package to hit the ground.
The final answer is:
A) The height of the package in 2 seconds is 226 ft.
B) It takes approximately 4.17 seconds for the package to hit the ground.