Question 5.5. Sandra throws an object into the air with an initial vertical velocity of 38 feet per second, from a platform that is 30 feet above the ground. How long will it take the object to hit the ground?
(Points : 1)
1 second
2 seconds
3 seconds
4 seconds
Yea, I just took the quiz and 3s is the correct answer
And why do you think it took 4 seconds?
(wrong guess by the way)
4 is not it I think
but 3 kind of looks reasonable
in this system of units, remembered only by ancient mathematicians, g = 32 ft/s^2 approximately.
so
a = - 32
v = Vi - 32 t
= 38 - 32 t
h = Hi + Vi t + (1/2) a t^2
0 = 30 + 38 t - 16 t^2
or
16 t^2 - 38 t - 30 = 0
8 t^2 -19 t -15 = 0
solve that quadratic for t, use the positive result (obviously it was also at zero height before it started :)
I think it's 3 too
To solve this problem, we can use the kinematic equation to find the time it takes for the object to hit the ground. The equation we'll use is:
y = y0 + v0 * t + (1/2) * a * t^2
Where:
- y is the final vertical position (in this case, it's 0 because the object hits the ground)
- y0 is the initial vertical position (30 feet)
- v0 is the initial vertical velocity (38 feet per second)
- a is the acceleration due to gravity (-32 feet per second squared) since it's acting in the opposite direction of the motion (downwards in this case)
- t is the time it takes for the object to hit the ground
Plugging in the given values into the equation:
0 = 30 + 38 * t + (1/2) * (-32) * t^2
Simplifying the equation:
0 = 30 + 38t - 16t^2
Rearranging the equation:
16t^2 - 38t - 30 = 0
To solve this quadratic equation, you can either factor it or use the quadratic formula. Factoring may not be straightforward in this case, so let's use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 16, b = -38, and c = -30. Let's plug them into the formula:
t = (-(-38) ± √((-38)^2 - 4 * 16 * (-30))) / (2 * 16)
Simplifying the equation:
t = (38 ± √(1444 + 1920)) / 32
t = (38 ± √(3364)) / 32
t = (38 ± 58) / 32
There are two possible values for t when using the ± sign:
t1 = (38 + 58) / 32 = 96 / 32 = 3 seconds
t2 = (38 - 58) / 32 = -20 / 32 = -0.625 seconds
Since time cannot be negative in this context, the object will hit the ground after approximately 3 seconds. Therefore, the answer is 3 seconds.
Question 5.5. Sandra throws an object into the air with an initial vertical velocity of 38 feet per second, from a platform that is 30 feet above the ground. How long will it take the object to hit the ground?
(Points : 1)
1 second
2 seconds
3 seconds
4 seconds
i think its 4 sec