# Thread: stuck on this question

1. ## stuck on this question

A raindrop has an initial downward speed of 10m/s and its downward acceleration a is given by

a= { 9-0.9 if 0<=t<=10 or 0 if t>10}

a. How far does the raindrop fall in the first 10s
b. What is the velocity of the raindrop after 1s
c. If the raindrop is initially 600m above the ground, how long does it take to fall?

Here is what ive done so far

a(t)=9-0.9t
v(t)=9t-0.45t^2+10
h(t)=4.5t^2-0.15t^3+10t

a. h(10)=4.5(10)^2-0.15(10)^3+10(10)= 400m
which is correct

b. v(1)=9(1)-0.45(1)^2+10 = 18.55 m/s
the answer is 55m/s. Is there something wrong here?

c. Since 600m > 400m, then it takes more than 10s to fall

a(t)=0
v(t)=10
h(t)=10t+600

0=10t+600
t= -60s ?

What did i do wrong for b and c?

2. Originally Posted by justin016
A raindrop has an initial downward speed of 10m/s and its downward acceleration a is given by

a= { 9-0.9 if 0<=t<=10 or 0 if t>10}

a. How far does the raindrop fall in the first 10s
b. What is the velocity of the raindrop after 1s Mr F says: There is a typo in the book. The question is meant to ask for velocity after 10s.

c. If the raindrop is initially 600m above the ground, how long does it take to fall?

Here is what ive done so far

a(t)=9-0.9t
v(t)=9t-0.45t^2+10
h(t)=4.5t^2-0.15t^3+10t

a. h(10)=4.5(10)^2-0.15(10)^3+10(10)= 400m
which is correct

b. v(1)=9(1)-0.45(1)^2+10 = 18.55 m/s
the answer is 55m/s. Is there something wrong here?

c. Since 600m > 400m, then it takes more than 10s to fall

a(t)=0
v(t)=10
h(t)=10t+600

0=10t+600
t= -60s ?

What did i do wrong for b and c?
After 10 seconds it has fallen 400 m. Calculate how long it takes to fall the final 200m and add this time to 10s. You're meant to realise that raindrop travels at a constant speed of 55m/s over this 200m distance.

3. for b, find the velocity at 11s....i.e. 1 second after 1st question

4. Originally Posted by justin016
...
a. How far does the raindrop fall in the first 10s
b. What is the velocity of the raindrop after 1s
c. If the raindrop is initially 600m above the ground, how long does it take to fall?
...
Here is what i've done so far

a. h(10)=4.5(10)^2-0.15(10)^3+10(10)= 400m
which is correct

b. v(1)=9(1)-0.45(1)^2+10 = 18.55 m/s
the answer is 55m/s. Is there something wrong here?

c. Since 600m > 400m, then it takes more than 10s to fall
...

What did i do wrong for b and c?
for 0<=t<=10
x(t) = 4.5(t)^2 - 0.15(t)^3 + 10(t)
v(t) = 9(t) - 0.45(t)^2+10

A. x(10) = distance fallen = 400m, If h is height, h(10) = 600m - 400m = 200m

B. I think that question b. as stated may be mistaken, it should have asked for the speed at t = 10 not at t = 1 . The velocity at t = 10, computes to the correct answer 55m/s.

C. At t = 10, using a. distance fallen = 400m,
h(10) = 600m - 400m = 200m

using b. v = 55m/s
compute time for last 200m

200m/(55m/s) = 3.6s
t(at h=0) = 10s + 3.6s = 13.6s