The distance s (in m) above the ground for a projectile fired vertically upward with a velocity of 4[a] m/s as a function of time t (in s ) is given bys=4[a]t−4.9t2 .

Question

The distance s (in ) above the ground for a projectile fired vertically upward with a velocity of 4  as a function of time t (in  ) is given by s =4(a)t-4.9t^2

Do not multiply. For example, if a=1 , then a is 41.

a=2

Find the answers to these questions.

find t for v=0

find v for t=4

find v for t=5

What conclusions can you draw?

Answer 1

that's an unusual way to calculate 4a as just adding on another digit

but if that's the problem then with a=2, 4a = 42

v=0 when t = 42/9.8 = 21/4.9 = about 4.3 seconds

v=42-9.8t = 0

v = 2,8 when t = 4

v=42 - 9.8(4) = 42 -39.2

v = -7 when t = 5

v= 42 - 9.8(5) = 42-49

it reaches a maximum height of 90 meters in about 4.3 seconds, then falls down to the ground in twice that time or about 8.6 seconds

velocity is increasingly negative after 4.3 seconds, at 4.3 seconds, velocity is zero, reaching about -42.3 meters per second as it hits the ground Conclusion? Move out of the way when before 8.6 seconds or you'll be paying the max deductible on your health insurance. 42.3 meters per second = about 94 mph. You might want to have some funeral expenses planned if you're a slow mover.

Answer 2

The distance above ground as a function of time is s(t) = 4[a]t - 4.9t². I'm not sure what value of (a) you are using, so I am keeping it general. You can substitute (a) in yourself, but keep in mind the meaning of (a) in this problem. 4[a] is not the product of 4 and (a), but rather the concatenation.

For each of your questions, we need to know the velocity as a function of time. We obtain this by differentiation and see that v(t) = ds(t)/dt = 4[a] - 9.8t.

Question 1: The time at which v = 0 is obtained by setting v(t) = 4[a] - 9.8t = 0. From this we see that t = 4[a]/9.8.

Question 2: The velocity at time t = 4 is simply v(4) = 4[a] - 9.8(4) = 4[a] - 39.2.

Question 3: The velocity at time t = 5 is simply v(5) = 4[a] - 9.8(5) = 4[a] - 49.