jonnburton
Junior Member
- Joined
- Dec 16, 2012
- Messages
- 155
Hi,
Could anybody tell me how I''m going wrong in dealing with this question on vectors?
A boat moves with a constant acceleration of (0.2i + 0.1j)m/s.
At time t = 10, the boat is at point A, which has position vector (30i-35j)metres
At time t = 20, the boat is at point B, which has position vector (70i-40j) metres.
Find the velocity of the boat when t = 10.
This is what I've done.
use \(\displaystyle r_10 = (30i - 35j)\) and use this as \(\displaystyle r_0\), given the time between this position vector and \(\displaystyle r_20 = 70i-40j)\) is 10 seconds.
\(\displaystyle r = ut +\frac{1}{2}at^2 + r_0\)
\(\displaystyle r_20 = 70i - 40j) = 10u + \frac{1}{2}(0.2i+0.1j)*100+ (30i - 35j)\)
\(\displaystyle 70i -40j = 10 u + 50 (0.2i+0.1j)+(30i-35j)\)
\(\displaystyle 70i-40j = 10u + 10i + 5j +30i-35j\)
\(\displaystyle 70i-40j = 10u + 40i -30j]/tex]
\(\displaystyle 10 u = 30i-10j\)
\(\displaystyle u =3i-j\)
However, according to the book, the answer should be 4i+12j; and no matter what I do I can't see how this is arrived at...\)
Could anybody tell me how I''m going wrong in dealing with this question on vectors?
A boat moves with a constant acceleration of (0.2i + 0.1j)m/s.
At time t = 10, the boat is at point A, which has position vector (30i-35j)metres
At time t = 20, the boat is at point B, which has position vector (70i-40j) metres.
Find the velocity of the boat when t = 10.
This is what I've done.
use \(\displaystyle r_10 = (30i - 35j)\) and use this as \(\displaystyle r_0\), given the time between this position vector and \(\displaystyle r_20 = 70i-40j)\) is 10 seconds.
\(\displaystyle r = ut +\frac{1}{2}at^2 + r_0\)
\(\displaystyle r_20 = 70i - 40j) = 10u + \frac{1}{2}(0.2i+0.1j)*100+ (30i - 35j)\)
\(\displaystyle 70i -40j = 10 u + 50 (0.2i+0.1j)+(30i-35j)\)
\(\displaystyle 70i-40j = 10u + 10i + 5j +30i-35j\)
\(\displaystyle 70i-40j = 10u + 40i -30j]/tex]
\(\displaystyle 10 u = 30i-10j\)
\(\displaystyle u =3i-j\)
However, according to the book, the answer should be 4i+12j; and no matter what I do I can't see how this is arrived at...\)