Danny lowers the sails on his boat. he paddles upstream at 19 km/hr. the current is still running downstream at 15 km/hr. what is the actual velocity of the boat? 34 km/hr, downstream 34 km/hr, upstream 4 km/hr, downstream 4 km/hr, upstream

upstream 4 km/h

Explanation:

Let's define "upstream" as positive direction for the velocities. Therefore, we have:

is the velocity of Danny paddling, which is positive because it is upstream

is the velocity of the current, which is negative because it is downstream

Velocity is a vector, so we have to calculate the resultant velocity. However, the two velocities are along the same direction (just with opposite sign), so their resultant is given by their sum:

and the positive sign means the direction is upward.

the velocity you are looking for is made up of two parts: horizontally velocity, vh, and its vertical velocity, vv. the actual velocity of the ball will be these two parts added together, and because velocity is a vector then they will need to be added vectorially.  

neglecting air resistance etc etc.,  

the horizontal velocity component will be constant (because there is no accelerating force in the horizontal direction.  

vh = 8 ms-1  

the vertical velocity component has an accelerating force: 'g'.  

using v = u +at where a = g = 9.81 ms-2.  

the vertical component of velocity, vv = 0 + gt = vv =9.81 x 2  

vv = 19.62 ms-1 . the zero appears because the virtical component of velocity at time t=0 is zero. remember, the ball was thrown horizontally.  

how fast it will be moving (it actual path (being a parabola )) will be the vector sum of these two.  

adding vectorally gives: -  

v = sqr root (8^2 + 19.62^2) = sqr root(64+384.9) = 21.18 or 21.2 ms-1

idk sorry i only needs point for apex

explanation: