The height of an object t seconds after it is dropped from a height of 550 meters is Find the average velocity of the object during the first 7 seconds.
A)34.30 m/sec
B)-34.30 m/sec
C)-49.00 m/sec
D)49 m/sec
E)-16.00 m/sec

Question

The height of an object t seconds after it is dropped from a height of 550 meters is  Find the average velocity of the object during the first 7 seconds.
A)34.30 m/sec 
B)-34.30 m/sec 
C)-49.00 m/sec 
D)49 m/sec 
E)-16.00 m/sec

Quizplus · Accepted Answer

To find the average velocity of the object during the first 7 seconds, we need to find the displacement of the object during that time interval.

The initial height of the object is 550m and after 7 seconds, its height can be found by:

h(7) = -4.9(7)^2 + 0(7) + 550 ≈ 222.7m

Therefore, the displacement of the object during the first 7 seconds is:

Δy = 222.7 - 550 = -327.3m

The negative sign indicates that the object is moving downwards.

The average velocity during the first 7 seconds is then:

v = Δy/Δt = -327.3/7 ≈ -34.30m/sec

So, the answer is B. The velocity of the object at any time t is given by the derivative of its height function. In this case, the height function is h(t) = 550 - 4.9t^2 (where g=9.8 m/s^2 is the acceleration due to gravity and the negative sign indicates that the object is falling). 
The velocity function is v(t) = h'(t) = -9.8t. 
The average velocity of the object during the first 7 seconds is then:
v_avg = (1/7) integral from 0 to 7 of v(t) dt 
v_avg = (1/7) integral from 0 to 7 of -9.8t dt  
v_avg = (1/7) [-4.9t^2] from 0 to 7 
v_avg = (1/7) [-4.9(7^2 - 0^2)] 
v_avg = -34.3 m/s (rounded to two decimal places) 
Therefore, the best choice is B.

The Height of an Object T Seconds After It Is