Question

An object dropped from a height of 290 feet will fall according to the equation h(t) = 290 - 16t^2, where t is measured in seconds, and h(t) is measured in feet. What is the height of the object after 1.1 seconds? How long will it take for the object to hit the ground?

a) h(1.1) = 275.04 feet; The object will hit the ground in 3.2 seconds.
b) h(1.1) = 273.74 feet; The object will hit the ground in 4.1 seconds.
c) h(1.1) = 277.36 feet; The object will hit the ground in 2.8 seconds.
d) h(1.1) = 279.64 feet; The object will hit the ground in 2.1 seconds.

Answer 1

The height of the object after 1.1 seconds is 270.64 feet. It will take approximately 4.25 seconds for the object to hit the ground.

Step-by-step explanation:

The question pertains to the free fall motion of an object under the influence of gravity, described by the equation h(t) = 290 - 16t2, where t is time in seconds and h(t) is the height in feet. To find the height of the object after 1.1 seconds, we substitute 1.1 into the equation: h(1.1) = 290 - 16(1.1)2 = 290 - 16(1.21) = 290 - 19.36 = 270.64 feet.

To determine when the object will hit the ground, we set h(t) equal to zero and solve for t: 0 = 290 - 16t2. This simplifies to 16t2 = 290, and t2 = 290/16, leading to t = √(290/16), which gives us approximately t = 4.25 seconds (rounded to two decimal places).PJ11