Time for a bomb to hit the ground

[tzek]

Homework Statement

Bush fir patrols sometimes drop small bomb to start a controlled burn off from aeroplanes. Peter was flying his over a forest at constant horizontal speed of 75m/s and at contsant altitude of 490m when he dropped the bomb.
A) how long does it take for the bomb to hit the ground?

Homework Equations

we have a displacement (490m) , an acceleration (gravity, 9.8 m/s/s) and a velocity (75m/s), so v = u + at could be transposed to give time, however I am hopeless at this. please advise..

The Attempt at a Solution

after some fiddling around with other formulae such as t = s/v = 6.53 s.. which according to the answers section is wrong.. they say 10s.. is this right? please advise me on this ASAP please..

 

[physixguru]

Welcome To PF.

When the bomb is dropped from the aeroplane it has some horizontal velocity which is equal to the velocity of the aeroplane i.e. 75 m/s.
Use concepts of horizontal and vertical components of velocity.Use accln along x axis=0 and accln along y-axis = g.Use s[y]: 490 m.

Now use simple kinematic equations.

suggestion= the simple basic formulae are very important but in these kinda questions they will not be aplicable becoz as there are horizontal and vertical components of velocityand accln involved.

 

[Moetasim]

I would approach this problem by first identifying the relevant equations and variables. In this case, we have the displacement (490m), initial velocity (75m/s), and acceleration due to gravity (9.8m/s^2). We can use the equation s = ut + 1/2at^2 to solve for the time it takes for the bomb to hit the ground.

Plugging in the values, we get 490m = (75m/s)(t) + 1/2(9.8m/s^2)(t^2). Rearranging the equation, we get 0 = 4.9t^2 + 75t - 490. Using the quadratic formula, we get two possible values for t: t = 10s or t = -9.9s. Since time cannot be negative, we can conclude that it takes 10 seconds for the bomb to hit the ground.

It is important to note that this calculation assumes that the bomb is dropped from rest (u = 0). If the plane was already moving at a constant horizontal speed of 75m/s before the bomb was dropped, then the time it takes for the bomb to hit the ground would be slightly longer. This is because the horizontal velocity of the plane would contribute to the horizontal displacement of the bomb. However, since the problem does not specify the initial speed of the plane, we can assume that it was dropped from rest and use the value of 10 seconds.