A dart is projected upwards at an angel of 20° with the horizontal. It has an initial velocity of 20 m/s. In how many seconds will it reach the...

I am assuming (in absence of any further information in the question) that the dart board is at the same vertical level as the point of projection. 

Given data: initial velocity, u = 20 m/s

angle of projection, `theta`  = 20  

Using the equation of projectile motion:

`y = u_y t - 1/2 g t^(2)`

where, `u_y`  is vertical component of velocity and is given as u sin(`theta` ).

 Substituting y = 0, we get,

t = 0 sec (initial instant) and

t = `(2usintheta)/(g) = 1.395 sec`

Thus, it would take about 1.4 seconds for the dart to hit the board. 

The point of projection is at a distance equal to range of the projectile motion. Using the equation for range,

`R = (u^2sin2theta)/(g) = (20^2 sin(2xx20))/(9.81) = 26.21 m`

Thus, the dart will strike its target 26.21 m from the point of projection.

Hope this helps.